So you remember the last class, we derived the Schwingler-Eisen equations, the equations of motion under the presentation, and as a trivial use of this, we computed the propagator, the two-point function of pi x with pi y in a free-scaler theory, and we ended up with, in momentum space, the propagated view came to be minus i by k squared plus n squared. And we ended the last class by saying this would be very good, except it was ambiguous because k squared plus n squared goes to zero on the shell, so this propagator was ambiguous because we needed to give it a better definition. And part of the purpose of what we're trying to do now is to approach to words that are giving better definition of navigation. Fine, let's do that. So part of the purpose of the next 15 or 20 minutes is to give this definition of the first model. Wait a minute, okay. We can go back to the path in time. You can remember that we are basically discussing the path in time, but starting with the observation that it can find by h t. Let me write that as dx, bar. Okay. And now we'll do this very often. Perhaps it's worth taking a minute to step back and ask, is this formula that we have defined very defined? Is this formula that we can now make defined? So if we take it up, is the path integral of the right-hand side very defined? We might be a little nervous because, you know, if a mathematician wants a well-defined path at the integral of any path, he wants the integral at the integral is 0 to infinity. He wants the integral to die off at infinity. That's a basic requirement for convergence. We've got a path integral is a lot of integrals. An integral for every x of t. And you could ask, does the integral to die off at infinity? And the answer is no, because the modulus of the integral is 1.  Now, as all of you know, this need not make this, need not in any physical sense make this path integral if defined. Because even integrals that have constant modulus can integrate something very rapidly vanishing because very rapid cancellation of phases. And that's the idea that this path integral makes sense even though it doesn't, the integral doesn't manage a large values because of rapid cancellation of phases. However, this is a very delicate thing. And it's a bit delicate to try to, for instance, use, in the last class we used the integral of a total derivative was 0. Is this really true when the integral doesn't die off at infinity? It just oscillates. It's a bit unclear. Yes. The rapid cancellation of phases only occurs in the classical integral. No, it will happen when you go to very large, it happens in the classical level. But in any situation where different parts of the integral have a rapid change in phase without significant change in magnitude. Yeah. So, in particular, it will also happen very rapidly across a very large value of field space. Yeah. Questions like this perhaps suggest it would be nicer to have a cleaner definition of the path integral. One in which we can more, it will create a confidence that we use, the manipulations that we're used to in the integral and sort of have great confidence in the convergence. So, what we now use to find a sort of better definition of this object. So, we are not going to provide what in some sense is the real definition. Okay, mathematically well defined to the path integral. The better defined version of the path integral. Okay.  And after each slicing, we inserted a complete set of states. Now, we worked with the, with the precision items. So, we could have worked with any basis. For instance, we could have worked with an energy, an item basis. And then we would have had all the energies from the lower bound. All our systems would be such that there's a lower bound in energy. Up to infinity. Most of our systems would be such that there's no bottom in the energy of the upper bound. Okay. And the expectation is that the very rapid cancellation in the very high energy states makes, makes the contribution of infinity well defined. But this is another way of saying what's valid. However, suppose we instead consider the following object, e to the power minus t distribution. In this object, in this object the cancellation, the fact that very high energy states and intermediate states don't contribute is manifest. Okay. The fact that very high energy states and the intermediate states don't contribute is manifest. Because such states are exponentially net. Okay. Now, more particularly what we could have done was to take, what was important is that there was a negative real part to the city. This object e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus t e to the power minus is equal to i times e to the power which means we are interested in going to this part, we are interested in going to that part of the complex plane in the definition of this function. We can do is to take this object, define it by this and then define the object of real physical interest by analytically continuing to Euclidean position. As we said, if we go exactly to this axis, we are not into the same immediate definition. So, what is the way in which we define our actual object is T Euclidean is equal to e to the power i pi by e to the power of the actual time, where we take the limit epsilon versus e to the power but we may need to keep epsilon in various expressions. This is our definition, T E, this is what we are going to try to do, we are going to try to define an auxiliary object, regarding this analytic function in T Euclidean and then obtain the object that we are interested in by analytic continuation. Pretty simple, pretty clear procedure. The first thing we are going to do is to go back to quantum mechanics and try to compute this object and see if it pans out, then it gives us a better definition. So, we are just going to repeat the kind of calculations that we have to perform. As you know, once we compute the infinitesimal evolution, then the rest is just follows. So, let us just compute e to the power minus delta t times h between x, x, n plus 1 and x z, this is the important part of the calculation. We know it exactly like we did before.  So, this becomes e to the power, you remember, we write this as product because of the infinitesimulation. This is usually becomes e to the power minus delta t v of x, n plus 1. This is usually becomes e to the power minus delta t v squared by u m.  Now, the integral of the overview is trivial to perform. So, now see the integral, so we do a bit completely square. So, what do we get? Well, let us see. So, this is e to the power minus of delta t by, so minus i, so minus i upon this delta x. That is one. Then I will get m divided by delta t, the whole thing squared. Just check that I got the cross term right, the cross term is minus 2 i with the minus sign. So, plus i, then p delta x and then m and delta x. So, that works. And then of course, we do this and add it in this new term. There was not actually there. It is this thing squared. This thing squared is minus, a plus, so we need a minus. So, minus delta x by m by delta t, the whole thing squared into delta t by 2. Integral over this is some number of the minus. What is this quantity? So, this is integral to p e to the power minus delta t into v of x and plus y. This contribution and this contribution here delta t by delta t is x dot. There is a overall minus delta t squared delta t, so there is an overall delta t. m plus m x dot squared by 2. And so, in the end what is left behind is the path integral. The x e to the power minus what is called x euclidean. Just definition. Where is euclidean? s euclidean is equal to v of x plus m x dot squared. Absolutely clear that this is a much better defined path integral than the other one. Why is that? Because s euclidean is positive. Or since we don't know whether v is positive or not. What I mean is that the contribution from infinity and s euclidean is highly suppressed. If the x goes to infinity we assume that v is either bounded or goes to infinity. And x dot squared is clear first. So, we are getting exponential suppression of crazy big forms. So, x going to infinity is going to be highly suppressed. Not by some delicate phase calculation, but just by the fact that the integral will match. So, let's take a look at this euclidean action once again. Let's take a look at this euclidean action once again. So, this euclidean action here was as we saw this object. And let's see if there is a simple way of obtaining it from the Mikavsky. That is of course, what we are saying about the path integral is i times s Mikavsky. Which is equal to i times minus m. This action is real, and this is a property. You remember we have this change, we have this relationship. t euclidean is equal to i times d Mikavsky. So, t euclidean was the t that appeared in the definition of this strange function. And d Mikavsky is the real action.  It was equal to minus of m x dot square by 2 plus 3 of x. Put this relationship in euclidean. I take the expression in the euclidean expression and I insert d euclidean is equal to minus i times d Mikavsky. What do I get? Firstly, I get a minus i from the major graph. But I've also become an extra minus sign because the d by d t picks up an extra minus sign. It's a bicycle. So, this becomes equal to i times m x dot square by 2 minus d of x. If I just make a substitution, t euclidean is equal to i times d euclidean. It's quite satisfying. The expression for the euclidean path integral is just a naive substitution of the expression for the euclidean path integral. Excellent. So, any questions or comments about this? Let me know. We're just completely analyzing the title here. Yes, sir. Basically what the answer is that just doing this mathematical trick makes the action the entire positive and the well-dependent. Well, we're physically involved because we know that that object is the compute. And we know that this object will not receive contributions from intermediate states at the time. You know, what we're doing in a path integral is breaking this up into small bits and summing over the contribution of all the intermediate states to these elements. We've arranged it. We've written it so that these operate right here will not receive significant contributions from intermediate states by their energy. Is this clear? No, it is. Then if we've done the other one here, if we try to compute, if we try to compute e to the power 3, okay, then we'll look at the output of that computing continuation. We'll have given us this path integral without the minus. And that would have been a terribly complicated. The combination of these configurations in infinity would manifest even though. Okay? We're just telling you that if you try to find the positive expression of this object with the positive, the path integral expression of this object with the positive and then try to, you would succeed. It's too divergent to operate. To admit the path integral. Okay? The next one is good. Is this clear? Yes. Is it similar to the problem that we had? It's going to be the same. We'll see. So it's used for avoiding the forms of the axis. Okay, exactly. We'll see this in just a minute. Off-shell wide? Mass. What do you mean off-shell, Mass? I said k squared is more equal to m squared. For the propagator? The last ten minutes, it has nothing to do with the propagator. We're going to get back to the propagator. Okay? Yes. Sir, the point of this is going to be avoiding the pole of the mass. We're going to add an i. This will add an i as well. Let's do that. Four questions. Yes. What we saw earlier is that if you do a given continuation of the sign, that is, you are going to give it the action itself. Yes. But from now on, you can just give it an analytically continuum action itself and whatever. We can, though. It's useful all the way. I mean, sometimes it's useful to go back to first minutes. You know, you can ask. For instance, what exactly is known by analytic continuation of the action? A function you can analytically. What function is the analytic continuum? His function. But what do we do by this? You know, it makes sense to talk about it. That's a well-defined mathematical. The other thing is a bit... That's not what it means. It's not that clear. Okay? We've seen as an observation that there's a trick to obtaining this. I prefer to word it and say, what we're doing is analytically continuum of this object. And then you get what you need. That's a clear statement. I think that's sort of a mathematical question. Yes. Is it always possible to analytically continuum something? I mean, in Kowski's access to the union axis, I mean, there can be branched out between the separate center, right? So, what do we talk about? Ah. So, in what we did here... In what we did here, think that there will... Okay. That's a good question. I think that we have sort of guaranteed that there will not... at least find the diagram perturbation. Okay? This analytic continuum is guaranteed never to have such... such significance. That... That makes very quiet words when we come to that. The point is, let me get... You know, you've got some... You've got some integral and perturbation here. And the only place where the integral is manifestly an analytic function of all external variables, except when the integral hits some singularity of the problem. Okay? And this analytic continuation is arranged... I will explain this much more detail. Because analytic continuation is arranged such that when they propagate this with the right ions, the analytic continuation can proceed without ever encountering the same. Any final diagram perturbation theory at least... Well, we'll prove this. Okay? I think it's more general statement, but at least the same pricing. Ah. Yes, please go. Could you meet me, sir, for a little further further? I think as long as we... The potential there does not have any non-analytic dependence on these things. We can always say that it... This is probably true here. It's probably true here. Yeah. Like, if you would, in this way, this is manifestly an analytic function of p. That... You know, that just is an analytic function of p. Why? Okay? See, some of us have got some of... Let me take the matrix elements of this between two energy elements states. That is clearly an analytic function. And then the matrix elements between any two other states is the matrix elements between energy items states times the inner products of that with the empty elements states. Now, the only possible way that could lose analytic dissipation would be because of the sum of exponentials. Is it that sum language? But it can't do that because of the exponential left. Unless you deal with two craziest things. Where the state has more and more overlap with higher and higher. The overlap with higher energy states grows exponentially. That would not be an omniscient state. Right? So, I think it's quite clear from this point of view that it will be. If there are similarities in the way in vx, nothing in potential that you could avoid any sort of non-amplicity but you could also have branch, that's not...  I don't say anything about the derivatives. All we were required was this dysfunction. All we required was that this function have a reasonable spectrum. Let's operate it as a reasonable spectrum. That was all that was needed for my output. We didn't talk about branch guards, poles, anything like that. This is a slightly abstract argument. We flash it out in propagation. Okay, I don't... At this level, it's just clear that there's an amplitude. Is that true? Okay. Okay, now since there are many questions of the propagator, let's get back to the propagator before we move on to whatever we need to say next. So now, applying the same technique, applying the same technique to... applying the same technique to a scale of truth theory, just by identifying more the kinetic term as more the potential term is, you easily say that if S Minkowski was equal to minus 10 mu 5 and mu 5 mu 2, let's say minus M squared by squared minus v of 5, the equivalent of 5 to the power of f. That's better. If somebody tells me about the utility, that should be... which is necessary for theory to be... not bounded from below, it's necessary for theory to make sense. You know, first as in the quantum mechanics case, you know it's my little math problem. Okay, let us repeat a computation of the propagator things up. Okay, let us repeat a computation of the propagator. Okay, let us repeat a computation of the propagator for this path. I'm doing it again just to give you practice with... you know the answer, right? It's one of the case questions. But actually, I'm doing it again just to give you practice with manipulating path. So what we're going to do, and this is now a legitimate operation. At least if there's a regular term. That is totally legitimate. You've got d5, you take d by d5 x, e to the power minus x. So this pi is a pi. The second object has... so delta of x minus y. That's one term in this case. And... time expectation value. The second object is what it's with. This is this. Let's set this to 0. So plus... minus del squared plus m squared pi of x. Propagated by the expectation value of 1. Let's call it that g of x, y of g of x, y. x, y. Obviously, the equation of minus del squared of del squared minus m squared of this is equal to... delta of x. What? What? This is the standardized equation. And... I'm writing this with sine. Sine and with sine because of the... minus and with sine. Somebody should copy that. You see, right? The m squared of this comes with the minus. So this is... minus del squared of x. Now we go to the momentum space. And this gives us the g of p is equal to 1 over 3 squared. Let me know. So the Euclidean propagator is simply 1 over 3 squared. Now, I understand how I can deny the Minkowski propagator from this expression. Now, notice, by the way, the Euclidean action has invariance under XO4. It's not an XO3 formula. Okay? Notice also, by the way, that the strength of computing a Euclidean action makes this... makes the bottleneck... look very much like statistical physics. Because what you're doing is summing over all the configurations of what looks like a spin system, weighted by some measure which you can think of as... which you can think of as... like the Hamiltonian, sometimes. We'll come back to this analogy as we proceed. But the fact... fact. So now we've got this propagator and we want to understand how, given that we have the propagator in Euclidean space, how we can compute the propagator in Minkowski? We do want to do the analytic continuation. Okay. Something I didn't say, but let me say now, is that it is natural to define not just the transition amplitude, the analytic continuation, not just of the transition amplitude, but of all operated insertions. So, suppose we define e to the bar minus, suppose we're defining the following object. So today on the side, let me define e to the bar minus d1 minus dmi h times x. And we'll go back to what we get. e to the bar minus d2 minus d1 h times x. And so on. Exactly like we did for defining operator is time-ordered, with a time-ordered operator. Except we use e to the bar minus instead of e to the bar minus i. Okay. Let's define this object here. Let's define this object here as the analytic continuation. Let's define this object as expectation value that you can detect. This function, I'll give it a name. g of d1, d2, some object with any insertions. Okay. It also depends on d, i, t, m. And it also depends on the states. And the states depends on the states. Okay. Without any insertions, the corresponding object was obtained by just setting ti is equal to i times t with Kowski i, tf is equal to i times t with Kowski i. Okay. We'll do the same analytic continuation to all the electrical simultaneously. If we do that, you see, we're then computing what we actually want. Because these will become the actual energy operation and set up with these states. And then we'll give us the actual time-order time-order operator product insertions we want. Okay. What sense does time-order mean when it has time and space? Because it is at equal value to space and now if I perform a two-second athlete, it's true of any one way that I am performing. Because just, it is true for the space coordinates. It is equivalent to space. And what, firstly what we're doing is defining the problem. Okay. Firstly what we're doing is we're trying to define the object which will analytically continue to the time-order operator product in many contexts. Okay. Do you agree that if I define this, if this is my object, and then on this object, I perform this analytic, which always, even when I write an i, i is always the power i by 2 minus 10 seconds. All of this. Okay. Do you agree that I may get back to the quantity I want? Yes. Okay. Now let's get back to your question. In quantum mechanics, of course, it was completely weathered by. There is a line, and I order that line. I time-order it on the line. Now, that's good. So, your question is that if I have a Euclidean quantum field theory, and I have different ways of slicing the integral, in fact, that's true, and it does work out. Say, one example of this that you may be familiar with is the difference between radial quantization and slice quantization. In radial quantization, the time-ordering of operators depends on which order and radius you're at. Okay. In slice quantization, it depends on where you are in the slice. So, the different notions use different Hamiltonians, different notions of ordering, but since they're both governed by the same integral expression, those two things will, in the end, turn out to be this. Okay. Yeah. Okay. Okay. Okay. I need to think a little bit more about your question. Okay. Okay. There's maybe something clear to say. Just a moment. I have something better to say about your question. There's something more than what I've said, but let me not try to think on the field. I'll be right back. Okay. But let's get back to this problem here. Okay. Let's go back to quantum mechanics. Do you see that if I take this object, this object, which is defined by these insertions, okay, and I continue the dice, I define this object, and I continue the dice in this way, then I get back to the object I want to complete. Okay. So, there is a natural object. There is a natural object to insert within the ingredient part of it, which is this object. There's a natural object to define within the ingredient part of it, which is that object. Okay. Okay. And with that operator insertion, with this insertion here, okay, with this insertion here, okay, now you can ask, why is the path integral expression for the computation of this object? That's how we have a suggestion. So, this object in Euclidean space is full. What path integral completes it? It's Euclidean, right? We know what the path integral is for completing this object. It's the path integral of the Euclidean action. And then, we have to do this step. But this step will insert an extra x. So, basically two points. Yeah, this is, yeah. This object here is computed by the Euclidean path integral, dx e to the power minus s, e to the power minus x, times x of t1, x of t, this is this object, only because it's analytic continuation. It gives us the object we want it to have. It's analytic continuation. Simultaneous analytic continuation. simultaneous analytic continuation in all times. Is it clear? But now we see something quite nice, that the object whose simultaneous analytic continuation in all times gives us what we want, is itself computed by very nice expression. If we want to compute operator insertions inside the mid-class key part of the table, it's often both best to define that actually often easier because you don't have to keep that factor so high. They're actually difficult to do in the calculation, and they do the analytic continuation. Is this clear? The moment. It's a little more than you can try to find. The moment is a mathematical trick but very useful method. Now let us employ this mathematical trick to the computation of the propagator. Let us employ this mathematical trick to the computation of the propagator of the scalar function. Now let us actually compute 5 of x, 5 of y in the mid-class degree. Instead, what the script is telling us is that we should just do this calculation. Can you make 5 of x, 5 of y in the Euclidean theory, and then analytic continuation. Now, we already know what 5 of x, 5 of y in the Euclidean theory because we just don't do it. In the moment, it faces whatever we spell plus. So let's write that down. Yeah, I'll go through this once very slowly. After this, we will, next time we do an analytic continuation, we just do it. We just, once, just to get the logic. The logic is a bit slippery. Okay. So what have we got? We've got the, let's look at the logic. T1 x, 5 of x, x of y, x Euclidean, y. The spatial parts of x of y are the same as the spatial parts of d because we have the tiny parts of d. This is equal to integral d dk over 2 pi d into the power i p k, k dot. Do you understand the formula? You know, the ingredient, I mean the momentum space correlator was 5 of p1, 5 minus p2 is 1 over p1 squared plus m squared times 2 pi to the d delta of p1 minus p2. Okay. And I put that plus value to the definition of the Fourier transform, the delta function, but make sure it's function of d of x, y and that's the remaining thing that we will do. Is this clear? These are things you know when you want to, we won't unless it's a question. Okay. So this is the answer that you can get now. Now, what are we supposed to do to get the answer, the object that we're really interested in? Okay. Our rule was, now let us forget about the x, spatial dependence. There's a dot product at 7 over k dot x minus e, which is the Euclidean one. Right. k is just a Fourier transform. This is just a Fourier transform. I've got a function of x and y, and it's the Fourier, I'm just Fourier transform. So it's k is 0, x is 0 plus k1, x1 is k2, x. It's Fourier transform. Formal Fourier, I mean. Point which I'm trying to focus on is k is equal to 0, x would have been dying, which would be a euclidean x. 0, p would have been k. What is p? k would have been k. Hang on, we're going to go through this. Yes. Yes, yes, yes. This is just an integral expression for the computer function given by this integral. Like no confusion of that. Now, what we want to do is to analytically continue this function. That's a clear procedure. It's a function to define my integral, we have to analytically continue. So what we want to do now, now I'm going to focus here, there are the space dependencies and the time dependencies. All the action is acting in time. I'm going to focus on time. So I'm just going to write this as x0, euclidean, y0, euclidean, and ignore the other dependencies. Okay, because they all just go along. Just so that you focus on the form. What are we supposed to do? We're supposed to take x0 increase and rotate into the power i by 2 minus alpha minus epsilon times x0 and that's it. Similarly, we're supposed to substitute this into the same expression. So we can compute that g, the real difference function in the middle of the space, x0, y0, where x0 and y0 are the real life in the middle of the space. Just math by mathematics. Okay, it's equal to dv, j by 2, 5, 8, 9, e to the power i, and here also I did not ignore the space dependencies. Okay, i k0, which you can give, let's call this x times x0 minus y0 e to the power i pi by 2 minus epsilon. I'm not writing that. Just not to clutter that. We're very interested. And we're also going to not write the dk, I'll just write dk0 in there. All the actions will happen. dk0 e to the power i pi by 2 is given by an integral. The integral goes along the k0, you can give me an expression that gives me the usual Fourier transform, the usual Fourier transform kind of expression as a function of x0 by 0. This is not the usual Fourier kind of transform and kind of expression, because this is an additional fact. But this is what I get, you know, I've stuck to it. So if I have to turn it into something that is more familiar to me, I have to do some valid mathematics to do it. So why is mathematics a method of writing? You see, what I'm going to try to do with the model, what I'm going to try to do is to take this contour and use Cauchy's theorem. You turn it into the following problem. Okay, for good. What I'm going to try to claim is that Cauchy's theorem tells me that this contour integral and that the integral over these arcs, but firstly, the integral over these arcs. So if I cut an integral like this, I can deform an integral like this down and like that. Provided there are no singularities inside. First let's check, are there singularities inside here? This function has singularities only on the complex, nothing on the imaginary. Since in my manipulation, this contour, which is this way, I'm turning it like this, not quite going to the imaginary. That's the point of this episode. Going through here and like this, I will never hit a singularity. Let me say this again if it was not. I'll say it again, it's important. I wanted to do an integral like this. I wanted to do an integral like this. What I do, what I'm going to do is to change the integration contour. I'm going to change the integration contour by using Cauchy's theorem. I can do that provided I don't hit a singularity on the mind. So this integration contour can be continuously conformed to this integration contour, plus these arcs here. So I start with this and I deform it to 2, 2, 2, 2, 2. And I can do that provided I don't encounter a singularity. Now all I'm doing is to say that inside this closed loop, the integral is zero by Cauchy's theorem. Is this clear? Sir, are these arcs in terms of the fact that they need to be high, high by 2 personas. Is that this kind of a circle kind of thing? So is that the reason why we have taken a circular arc or we could have taken it? We could have taken it. This is something, you know, an infinity. Now we want to check that the things at infinity match. Okay, so now for one sign of this, that's the logic for that equation. First let's work on the algebra and then we can answer that. Let's see. Let's assume first that this is positive. Okay, x here minus y here is positive. Okay, then let's look here. This guy here is basically i. So if this was a real number, this is actually i. That's i, which is minus. Okay, as we change this, this, we will change the real part. But can you see that the, that the, that the real part is always going to be, always going to be negative. Let me do the following. Let me, let me, let me, let me, let me get back to the next class about why we get, why these contours can be, because I've made an argument that there's an element I don't believe in. I fooled myself. I'll get back to you next class. Okay, about, I'll give you a proper argument for why these contours. They can be, no, there's a good argument I just got. Suppose that were the x. Okay, suppose that were the x, then by rotating to this contour here, then by rotating to this contour here. Okay, we are now exactly killed. This e to the power i pi, because we're rotated by e to the power minus i pi. So this exactly kills that. And now we have this, the following expression. Now we have the following expression we have, okay, and so gm of zero is equal to, what is it? Firstly, after we do the rotation, we've got a substitute in k zero e to the power n is equal to, now it's the inverse candidate. So minus i e to the pi k dot x times y divided by, and what have we got here? We get what was k zero squared. It was k zero squared, but this k zero now has become the inverse of this. So e to the power minus i pi minus two epsilon squared plus k i squared plus x squared. You see this minus i being from the measure factor, and this rotation is, the fact that we rotate to this contour here. I'll get back to you about this thing, okay? We don't want to step. You can ask what you mean. Now what happens to this k dot? So e to the power minus i is minus one. So this is now the effect of Fourier transform. So we get one over minus k zero squared times e to the power i two epsilon. Two epsilon. Epsilon to epsilon. Epsilon is just a positive number. It's a small positive number, okay? Plus k i squared plus x squared. Now we can expand this e to the pi epsilon. So this is one over minus k zero squared plus k i squared plus x squared minus i times some number. Epsilon prime was epsilon into k zero squared. The only thing, the important thing about epsilon is it's in sign. This became minus from the plus because I expanded. This is one plus i epsilon, and then it was minus. Is this clear? So this gives you the rule. This analytic continuation gives you this rule. It basically tells you that once you can justify and neglect the contours and infinity, okay? It tells you that in the Fourier transform, in the Fourier transform, what you have to do is to do the reverse. So we have e e to the power i by two epsilon times three m. The net result of this manipulation is that if you've got a Green's function in euclidean space, you've got it as a function of k euclidean. This is just the Fourier mode of the euclidean. What you do to get the Mankowski function is the reverse rotation. So e to k e is equal to e to the power i pi by minus i pi by two plus minus pi by two. It tells you that all these polar particles which are deltas and deltas, k zero is like e to the minus i theta, where theta would be less than pi by two minus epsilon. So it would be like e to the i theta where theta is like in the first quadrant, plus theta plus i sin theta, e to the i e to the y sin theta, e to the minus sin theta, sin theta would be positive deltas, k over point b would be negative deltas. This is something that is going on. However, let me not endorse it completely. I'll get back to you next class about why this one. Why this one? Let me hold on to that. I want to go tell you an element of that. It's okay. So after this big machine I owe you, after this just to make the contour neglect, which I owe you, we come to the following conclusion that what we should get and where we have to is that we also have this factor of minus i, that is from the measure of the content. So now this here, so in the correct, in a real mechanism, in Kowski's case, Fourier phase is a complicated minus i divided by K squared plus M squared. This is exactly what we got by direct computation. Except we didn't have that minus i. So the minus i epsilon is the result of working with a well-defined path detector, one that you obtain in the Euclidean space and then analytically continue. So here we are rotating it, we are closing it also in this direction. And we close it in the other direction, they still wouldn't have more to bring because when the rotation product will like Km, Ke going to be to the i by going to minus i. Yes, absolutely. It's very important which direction we do the analytic. So it depends on that because that is also very mathematical. No, no, no, no. Not that, yes. So which one did we have to do? We had to do the rotation that cancels the analytic continuation of time. What chose the analytic continuation of time? The thing was chosen so that we wanted e to the power i h to become, correspond to the power minus h to u. If we did the opposite one, we would have had plus here. It's guided by the basic principle, that the well defined path integral is that for e to the power minus t times h. This is also actually by the way, I mean the resolution of this contour thing because this object is only well defined if t is positive. So I would get confused about what chose the sine wave 0 minus 0. This is going to be the heart in that contour like that. This is going to be the heart. But let me think it through again. This object is well defined for positive t and ill-defined for negative t. That will become some sine of h 0 minus 0. But let me say it properly. So what are we going to do with this particular analytic activation? You're assuming t is positive. That's basically the heart. So that's the kind of contour which can choose for the analytic continuation. That's right. This is going to give you the neglect of those terms. But let me say it carefully. This is basically the heart. Exactly. Every evolution step goes forward. You're not going to go backwards. Yeah. But let me say it properly. Okay, great. Any other questions or comments about this? So far in this class, we've understood the analytic continuation of the path of t. And we've understood how this analytic continuation also gives us the i-absorbs of the problem. The usual i-absorbs of the problem. Okay, exercise. And if the canonical, this is something that you've already done in your first course, just to remind yourself, show that it's the canonical way of computing time-ordered, pi of x, pi of y, uses this with design. Now, you get the same answer. If you just use canonical quantization, let's start with the first course. And just compute. Okay? As you all know, it's useful for this purpose to write down an integral expression for the detail. As an integral. Okay? Do that. Sure. But maybe by tomorrow, I'll send you a list of exercises to do. This will be one of them. And that's something you don't mind. I'll come to you and ask you. A list of exercises. So that's what the other thing about. Okay, great. Fine. Any other questions or comments about that? I have a question for you. I mean, how do you sense the partner and the integral function? Yes. I mean, you can have so-called relations as well as the space as well. Choose that. None of them. It will choose that. So your analytic continuation, it's true. Choose our particular size. Nonetheless, it's also true that different expressions that have different Minkowski and interpretation have the same opinion expression. And therefore must be the same. And this question was, how do we understand a priority? That these things shouldn't be the same. Again, I'll think about this and see if I can figure it out. We have to formulate the question properly and then have something to say. I feel there's something more to say about this. Okay. Other questions or comments? Let us move on now with analyzing partner names. So we've understood how to analytically continue. By the way, this analytic continuation has some twists when we deal with fermions and some twists when we deal with agents. Okay. But let me get to that, those twists after I finish saying everything I want to say. Before we go to the complications, let me say the basic things. We'll talk about these twists at the end of this class. The key to punch back on the gates will bring that if you are a well-defined pathet type group, you will have to analytically continue not just where we're doing but also the contour of integration over easy. Everything that has a zero index will have to be continued. We'll see how that works. Okay. But let's postpone that for a moment. Okay. Now I want to continue to analyze formal properties of the pathway. So, in the last class, we analyzed the streamerized equation. In this class, I wanted to try to understand how no-terse theorem works inside pathet type. We've got some field theory. For my freedom, we'll say it's field theory of the scalar fields. But it doesn't matter. We've got some field theory defined by the pathet type d5 e to the power of 0. How does this field theory has a continuous symmetry? What does that mean? That means that both the action and the measure or really all the streamers the product of the e to the power of 0 says that the measure usually works in the way that both the action and the measure and the invariance I'm going to change the variables so that phi is equal to phi tilde plus it's a lot better. I'm using very compact notation. There will be many scalar fields. F could have depended on some position that F could have depended on some position. It's whatever, some functional of all these variables. I'm making a symmetry that's an infinitesimal symmetry. It's a continuous symmetry and the infinitesimal part of it may not be ideal. Suppose under this change of variables when I run this back into the pathet type. The functional form of the pathet type remains unchanged. Which means that under this change of variables if I do this planning again this object remains d phi tilde. Is it equal to d phi tilde e to the power minus s let me emphasize something. In any integral you can always do a change of variables. That change of variables does not change the value of the integral as a number. That's just a property of integral. So for any change of variables this quantity will not change. But in general if you do a change of variables it will change in functional form. If you're doing integral x squared and you do it as a x squared is equal to y squared that will become integral y to the power times the measurement. So it will change the functional form. The answer will change. The functional form will change. But we're never forgetting from making changes of variables in integral but symmetries are those special changes of variables such that it leaves the functional form of the integral in pathet. That is you have the same integrand x in new variables as well as integral. When that happens this is said to be a symmetry of integral. Definition of symmetry. Any questions or comments? Suppose we have a symmetry. Suppose we have a symmetry in our x. I want to deduce the consequence of this for the for the operator insertions etc. In order to deduce this consequence what I'm going to do is is to take this and make the change of variables y is equal to 5 tilde plus epsilon of this change of variables is no longer a symmetry. For instance, an epsilon was like a refacing of a 5 tilde and now made a local refacing of a 5 tilde which is not a symmetry of the action as you very well know unless you also do something with a gauge beam or something. No gauge beam. This is no longer a symmetry of the action. So suppose I call this z z is equal to this object. Now z because under any change of variables the number means it very much. z continues to be given by some part integral b 5 tilde times e to the power minus s tilde of I've just said nothing because s tilde is a different function that I'm not saying. But now let's say what we can say about s tilde. What do we know about s tilde? We know that s tilde reduces to s when epsilon is constant. Therefore it must always be possible to write s tilde as it is a 5 tilde plus integral d over epsilon times sum j d. Because this j d means sum function. You could ask why aren't there more you could ask many things about this. You could ask why is this happening upstairs or downstairs. You could ask why don't you have more terms more derivatives than epsilon? The answer is you could. But if you didn't you could integrate by parts you could do those extra derivatives. You have to do the derivatives. I'm checking. So the change where it is can always be written in this form. z was equal to this but z was also equal to this object thing. One has 5 tilde now the other has 5. But this is an integral of integration. So you see by expanding this to first order you see we conclude an integral d pi tilde e to the power minus s of pi tilde into 1 plus epsilon j mu is equal to integral d pi e to the power minus s of pi. Because these are both z. But the first term this one here is equal to this so we conclude first thing that very good. Yes. What we conclude is so what we have done is of course integrated by parts and what we actually can do is that epsilon that's d mu j mu. Therefore it's true at each point. Because we can take epsilon to be very big take epsilon to be very big very big to be very big. Very big to be very big. The only way this can work same kind of argument we use when we do it when we get equated to a motion theorem of variation. If this is true by multiplying any function that's just better than expected. So we conclude that within the part of the effort expectation value of d mu j mu this is nice but we really want to conclude compute one point functions. Object is just one insertion however we often want to conclude let's redo our variations let's redo our variations in the presence of many insertions. So suppose we had this object here that's o of pi of x1 o1 o hand of pi that got some local operator insertions in the positive. What does local operator mean? It means some functional of pi that depends only on pi at x1 and its variables. Inside this one. So suppose I got this here when I do my change of variables suppose I started with this suppose I started with this here o1 of pi when I do my change of variables when I do my change of variables okay when I do my change of variables this object here this object here will in general pick up will also change so when I write o of pi and I put pi is equal to pi plus delta pi delta pi this will change to some new expression in terms of pi differing in order actually okay so when I rewrite what's 0 do you see what we're getting is integral d mu epsilon x mu times o5 o151 when is that lecture? it's here in 2 minutes so call us then the second term has none of this plus delta o15 x epsilon o2 o1 and so on so when we conclude from this I'm a little bit fast you try to fill it expectation of j mu and mu with o1 to o1 plus delta o1 o2 o1 o1 delta o2 o1 and so on is equal to 0 is the statement that the insertion of the derivative that the divergence of current presently of course this kind the fact that there was an object which 1.1 should manage this is not as clear it's between any states expectation manage j mu j mu m is the quantum of Northus god the existence of symmetry implies that the current and the more interesting the fact that in the modern game insertion of derivative with various operators related or equal to sums of changes of those operators under the symmetry object of sort of war identity extremely extremely useful identity in studying all kinds of quantum field theory notice that both Northus theorem see if you write Northus theorem plus this war identity in about 5 minutes 2 strips of the black wall you might notice that you know if you go and look at Goldstein's derivation of Northus theorem even in classical physics it's still it's such a simple theorem even it's quantum generalizations or something have the derivation of the war identity in all field theory control god it's this however you have to complicate your life I have a new exercise for you the exercise is use a chronicle of opulation you've probably done this before but I want you to remember and see how these two work together as you will see much easier to get these identities to derive them and get them right in the path of technical representation notice I wanted to explain the connection between this way of thinking the way of thinking of current differentiating with respect to gauge field if you connect to the background source also explain conservation of stress tensor from this point of view we'll go through that in the next class okay next Monday I will not be able to do this class next class I suggest once again next Wednesday Friday is the holiday Friday is the holiday okay so next Wednesday yes please hurry next class next Wednesday


Daily Tech News show is made possible by its listeners, thanks to all of you including Hector Bones, Tim Ashman, and Johnny Hernandez. Coming up on DTNS, Nicole Lee has great ideas on easy smart home gifts to get people even if they aren't that tech savvy. Plus, Sony makes motion capture cheap and easy, and the end of the year music streaming recaps are here, and we will admit what tops our list. This is the Daily Tech News for Tuesday, November 29th, 2022 in Los Angeles, I'm Tom Merritt. I'm Ben from Studio Web, and I'm Sarah Lane. From San Francisco, I'm Nicole Lee. And I'm the show's producer, Roger Jen. Oh, Nicole, thank you for bringing us like an accessible, not accessible so much as like wide ranging gift guide today. I can't wait to talk about it. Very wide range. Yeah, no.  It's perfect for those folks who like they went through all the black variety sales and they're like, I still have a couple of people on my list and I have no idea. Nicole's going to take care of that for you. So just hang in there. Let's start with the quick hits. Twitter updated the COVID-19 section of its transparency pages to say that, quote, effective November 23rd, 2022, Twitter is no longer enforcing the COVID-19 misleading information policy. End quote. Now, starting in 2020, Twitter began labeling posts with disputed information about COVID and removed posts that were demonstrably false. Twitter's community notes program, formerly called Birdwatch, will continue to add contextual notes to post about COVID. Yeah. So it's up to the audience now. India's central bank announced it will extend the test of its central bank digital currency, the E-Rupi, one of those CBDCs we've been telling you about forever. It's going to extend that test to retail starting December 1st. More local banks, the State Bank of India, ICICI Bank, Yes Bank and IDFC are going to participate in this retail phase of the pilot in four cities, Mumbai, Bengaluru, Bhubaneswar and New Delhi. More banks, cities and customers will be added as the test goes on. The central bank began evaluating the digital currency for the wholesale market last month. So this is the expansion into retail. The UK's proposed online safety bill will be amended to remove the obligation for social platforms to take down legal but harmful content. The government states the change affects platforms like Facebook, Twitter and TikTok is preserving free speech and giving people greater control over what they see online. UK cultural secretary Michelle Donnellyn says the amendment ensures no tech firms or future government could use the laws as licensed to censor legitimate views. The bill is due to return to parliament on Monday, December 5th. Man, that thing's taking forever to get through. We'll see. Wall Street Journal reports around 4,000 shipping containers containing solar panels have been detained coming into US ports and more are being held up on the other end in the exporting ports in places like Vietnam and Malaysia. The delay is caused by US customs agents enforcing a new law that requires that no solar panels contain parts made in China's Xinjiang region. Most panel makers are sourcing parts elsewhere, but they still have to show documentation to prove it. Wall Street Journal estimates around 23 gigawatts of solar projects have been delayed in the US so far this year. Yesterday we told you about OpenAI's algorithm that could play Minecraft. Today we have news of Nvidia's MindDojo. That's the algorithm that won the company an outstanding data set and benchmark paper award at the Neural Information Processing Systems Conference. Investor can write in natural language what it wants MindDojo to do, like build a portal and then enter it. And MindDojo can execute it in a game. What kind of portal though? I mean you gotta be specific. A cool one. You know, another portal, something like that. Alright. AI's. They're just gonna be playing all the games soon. Alright, we will then become virtual avatars. We might. Getting closer than ever.  The sensors are small. They're smart watch size devices. They fit on a charging case the size of a large smartphone case. The sensors connect to a smartphone running an app from Sony, which then records movement data in BVH format and can be exported as a recorded MP4 video. So you can use the app's avatars or you can use your own VRM avatars if you so desire. You kind of have the choice there. The app can also transfer motion data to a PC in real time using Unity, Autodesk, MotionBuilder, some of you are very familiar with both, might be kind of exciting there. An STK will come out December 15th to let developers integrate Mocopy data to apps. Reservations will begin in Japan in mid-December for an on sale date in late January. Mocopy will sell for, and this is actually I think a very important part of this if you're excited about it, for 49,500 yen, which is approximately 360 US dollars. Yeah. Under 500 dollars you can do MoCap for an indie film.  I think this is probably a bigger deal than people are making it. It's a little bit of a beginning to look like CES kind of project, right? It's like, oh, it's only available in Japan. Oh, and it's not a PlayStation from Sony, so I can't hook it up to my games. But this is going to make motion capture accessible in a way that it hasn't been. And whenever we see things like audio recording, video recording, et cetera, graphics become more accessible, you start to see an explosion of new kinds of content. And I think the important, the thing that popped up to me as I was watching the video is that it also seems very user friendly. Like it looks very attractive, easy enough to use. It looks like from the video, like it's all kind of clearly laid out. Like this is what they had. This is for the years and this is for the arms and legs and so forth. And if it's easy to use and it's affordable, that's enough, I think. People are going to find all kinds of weird, unexpected things to do with this, right? Yeah, yeah, my first reaction was like, OK, the avatar stuff I can get.  And I was like, OK, but yeah, let's think about how this was, I don't know, how many years it wasn't that many years ago that people were like, this whole movie was shot on an iPhone, you know, or a smartphone. I feel like this is it's sort of it's the next version of, hey, you can do this with pretty cheap software. You know, if you compare this to like going to some motion capture studio, not that long ago, like it's not going to be $360 goes. Yeah. And don't get me wrong, it's going to come out and people are immediately as soon as they get over the excitement, critique how it's not as good as, you know, the professional things and start like pushing for improvements to make it smoother. And those improvements are going to come and eventually people are going to complain that I have to attach six things. I just want one thing. And then there's going to be a development like that's just the way the stuff goes. But we're at a point where this is a thing you cannot do easily right now. And this this implementation of the technology is probably going to democratize it a little. And I think that's significant. Yeah. And I will no longer be appearing on DTNS as me. I would be an avatar as soon as I get this. This is not the weirdest idea. I know, right? I mean, at least just to give it a shot. I do it. Yeah. We might have to get one of these once they're out. What's available?  It's so convenient, but is it fair to the artists? Am I overpaying? Am I getting ripped off? We have some good news. The UK Competition and Markets Authority, the CMA, published its final report on its market study of music and streaming services. Now, the CMA's job is to find antitrust stuff. They if they have a bias, it's towards finding something is wrong. And they didn't find anything wrong. The CMA found that music prices have fallen by 20 percent as a result of competition in the music market because you have multiple good services. While it did find that major artists got the most money, that seemed to be because of us. We're streaming 60 percent of our music from zero point four percent of the top artists. The CMA found no evidence of excessive profits. Average royalty rates have actually risen for artists from nineteen point seven percent in 2012 to twenty three point three percent in twenty twenty one and for music writers from eight percent in two thousand eight to fifteen percent in twenty twenty one. So with that in mind, let's talk about the end of your music promotions coming from the three biggest streaming music providers. Yeah, so there's Apple, of course. Apple seems to be first out of the gate with Apple Music Replay. You can find it at replay dot music dot Apple dot com. You can sort of search for it online or perhaps find it in your iOS app, although I couldn't.  You got some chart views. You have some top playlists. You can also share your highlight reel in images with your stats, which is very much the point of all of this. It's an easy social media post type feature. YouTube also announced its twenty twenty two recap feature. You get to that supposedly by searching twenty twenty two recap, either in YouTube music or the main YouTube mobile app seems to be still rolling out, so you might have to wait for it to show up. It shows you your most watched or listened to artists, songs, videos and playlists, highlights, artists you may have discovered before they got big kind of make you feel like you're an insider and has a music personality feature, which tells you your music vibe. It can integrate with Google Photos as well. So in when you want to share your results, you can integrate your own photos into those shareable versions. If only somebody would tell me what my music vibe is. It would really help me out. Yeah, yeah, it is. Of course, the big one is Spotify is wrapped, which is still to come, probably shortly after the first of December. It was just last year where I was like, what is wrapped today? What is everybody talking about? It's a big deal. In the meantime, developer Anshu and Sean Taboo created an app called InstaFest. If you authorize it to view your Spotify account, it'll take your listening data and create a kind of cool three day Coachella-like festival poster with headliners based on your most played artists, which is very cute. I've seen it passed around quite a bit, maybe a little too much Twitter and Instagram, but but all that aside, time for everybody to spill. What are our top artists? Who's in our play fest? All right, you want me to go first? Yeah, go. What would you like to know? You want top album, artist or song? Do you want to go like number three on one of those lists? What are you looking for? Well, Tom, what's your top album of the year? My top album is Anti-Fragile by Lucera Femme. OK, OK, and you're using Apple Music. Yes, and I'm using that's right. I'm using Apple Music Replay because you're also an Apple Music user. Yeah, you know, so a couple of things that I have to say, like the Spotify shows it all in the app, but Apple Music, for some reason, kicks you to this website. Even if you go through the app, it makes you go to the website. So I mean, that's different. Also, like I guess I don't listen to that much music. It's only like 3000 minutes versus like all these other people that have like tens of thousands of minutes. But yeah, so like the top song on my list is Taylor Swift Midnights. I mean, yeah, very of the moment. Yeah, yeah, indeed. Current trend, Sarah, what about you? What's your top artist? Top artist is Kendrick Lamar. He had an album out this year. So, you know, that obviously helps. But I would listen to him anyway. I'm trying to go back to something that shows me the minutes. Listen, because Nicole, I'm kind of with you because of podcasts. My music listening is sort of at an all time low. And it's not because I don't like music. I really do. Mostly if I'm in my car, I'm like, oh, it's music time. Yes. In the car, in the car, which doesn't track. Which you know, I'm using carplay, I would. Yeah, but I don't know. Otherwise, yeah, I feel like I'm like, wow, I would have been like way in like the 20,000 hours. You know, I'm like, yeah, I'm kind of listening to podcasts. Yeah, I would actually be a better metric for me. My minutes were like 13,000 or something. That's more than me. Yeah. Yeah. Yeah, but I listen to a lot of podcasts as well. I think I would have listened to more. A lot of this is music that I play prior to it's a thing going live because I just put music on. You have to know. Yeah. Just get you in the mood. Yeah, it just makes sure people know that the Discord stream is working without me talking. This isn't really, you know, related to, you know, top artists of story or of songs and albums per se. But a few years ago, I remember a friend saying, oh, Sarah, like, I can't even run to music anymore, you know, because he'd like to run jog. And I was like, I can't even imagine not not running to music. I would just, you know, I wouldn't be able to like keep a pace. And now I can't listen to music while I'm running. Oh, you're there.  Yeah, like it's like I need to like, I need to get into a story. And then I have more fun. Welcome. Now you understand. Yes, I do. I was not that friend this way. She was not sub tweeting me. No, no, I certainly not. And, you know, I wouldn't be the only person to either. I'm the kind of person that will listen to the same podcast episode over and over and over again, because I like it so much. Yes, I'm that. I don't know that I've ever done that. I am that person. Oh, that's kind of cool. But that's sort of, you know, it's like that comfort movie that you watch every year and same idea. So we highly encourage everyone to listen to this episode of Daily Tech News Show as many times as you want. And then tell us about it on social media. You can get in touch with the DTNs audience on Twitter at DTNs show on Tiktok at Daily Tech News Show and on Instagram at DTNs pics. That's DTNs P I X. Well, Roger Tang has been in Yeoman's work putting together folks to tell us about gift guides this year. We've covered gift ideas for games with Trisha Hershberger, home theater with Patrick Norton, TVs with Robert Herron. But we're past Black Friday now, and you may have a few people on your list that you're having a hard time figuring out. If they have a home, we may be able to help you. Nicole has been looking at options for people who might not even be that tech savvy, but would appreciate a few things to make their homes a little smarter. Nicole, how did you come about these pics? Yeah, so I wanted to make these pics based on a wide range of, I guess, people in your life. So I have a pick for the cook in your life. I have a pick for, for example, like, you know, I think everyone should have an air purifier these days because, you know, pollution and stuff like that. So I have a recommendation for like a smarter air purifier, for example. And I have a couple of other picks for just, I think, like you said, everyone has a home. Everyone has electricity. Well, most everyone has electricity and outlets and things like that.  Excellent. Well, what are we starting with? Yeah. So the first thing on my list here is a smart outlet. So the easiest way to smart up any home is to get one of these little smart outlets. And they're very inexpensive. I think you could get like $24 for four or something like that. So these little things, any appliance that you plug into, it can instantly be like a smart appliance. You just, all you have to do is just like connect the outlet to like your phone through an app.  And you can program it to come on at a certain time in the morning. This is very cool. What I use it for every Christmas, I plug my Christmas tree lights to a smart outlet. I do it with exactly this smart plug that you're showing here. I did it like this weekend. Yeah. Yeah. And it's super easy.  And then because it turns out turn on the Christmas lights, turn off Christmas lights. It's so easy.  So it's super easy. And I mean, for anybody, I feel like who, you know, I'm kind of in the the Hube hub, you know, ecosystem. But it's like, if you don't have that built out, this works the same way in a pinch. Yeah. Yeah, especially like you said, like if someone doesn't doesn't have any smart, anything in their home, can't one of these things. It's like super, you know, low stakes. All right. What if they what if you want to get them into the Hube family? You mentioned you speaking of the Phillips Hughes. The other thing, if you want to spend a little bit more money, it's like a building to really build out a whole like smart lighting system. I love the Phillips Hughes system. This one, my favorite, like smart light smart light bulb systems. I especially recommend the Phillips LED smart bulb star kit, because it has like the multi color bulbs.  But I love the multi color ones because you can set like, you know, millions of colors to a room. So you can like warm moody lighting for like a cozy night in or like rainbows for parties or whatever you want. The companion lets you create timers so that, for example, or routines as well. So for example, you can set it so that the lights will gradually turn on in the morning to wake you up, because sunrise alarm, for example, I do, I do this every night because I'm a Hube person from 11 to 11 20. Yeah, lights start going down. Like if you're not already asleep, sir, you better get ready. And it's really helpful. It's it's it's a good way to like sort of lull you to sleep or wake you up and depending on how you want to start your team. And I also really like like turning it on when I'm on vacation. When we're both on vacation, I'll turn it on. And I mean, I don't know if it really helps per se, but it sort of simulates Oh, someone in the house or something like that. I don't I don't know if it's, you know, Warren's robbers or something like that. But maybe it does, right? So and I think that also the addition of the of the hub, the hub itself, you could have like 50 lights can connect up to like a single Hube hub so you can really outfit your entire house with like. And yes, matter is going to make that hub less necessary in the future. But for the time being, it's going to make it easier. And that's one of the things we're talking about. What about the thing that actually just showed up at my sister's house? I hope she's not watching as a present minutes ago, because I definitely bought this for her. I think it's sorry, I'm looking at the list here. Yeah, so, yes, robot vacuums. Will they be as efficient as like an actual vacuum? Probably not. But they do help out for like the occasional mid sort of like in between cleaning sessions, kind of a kind of a test. So my favorite robot vacuum is the iRobot Roomba 694. And I like it because it's kind of afforded. It's fairly affordable for a robot vacuum and it works great.  And it's the app is really good. The it's really easy to use, even if you don't really aren't super tech savvy, the app is really easy to use. You can program it to like certain parts of your house. It's connected to your Wi-Fi network. You can create a cleaning schedule for seven days. So, for example, like in the morning when you're when no one's in or at night. And also the better life on this thing is actually pretty decent. About 45 minutes to I think 90 minutes, depending on how hard it works it. So, yeah, I definitely recommend it. I don't have this latest Roomba version, but the Roomba has changed my life.  It's it doesn't replace a real deep clean. Yeah, but for kind of like every day, especially if people have kids or pets or, I don't know, you just have a dusty house or something.  And you spend less time cleaning. I really do. You were like more time. It's like automated robots and warehouses. You spend more time doing the things that you were supposed to do in the first place. Now, I have a Koeh air purifier, which I know, Nicole, you at least used to have, but you're you're recommending a smarter one than that. So I have both. I have the Koeh and also that doesn't call the Mila air purifier. This is like deluxe luxury air purifier, which, you know, depending on how you want to spend your money. But I really like it. And I think if you even have something like this, like really nerdy and into like statistics and like factual data about the air content in their house, like they will love this. It gives you all this data of like how much like particulate matter is in your air and like carbon. And it's all these sensors, too. It will tell you like what the level of carbon monoxide is in your home, which is very important, by the way, the VOC level in your volatile organic compounds, the VOC level in your home, how humid your home is was also very important, actually, for like mold and mildew reasons. And I love this Mila air purifier because you have the option of picking out from several filter options. So the basic one is like the basic breather filter. This is like filters you sort of buy with the air purifier. There are other filters, for example, like there are filters for pet livers. So if you have a cat or a dog, you can get special filters that will really filter out like stink and like odor, which is definitely a problem if you have pets. There's also a specific filter. If you have someone in your home was really allergic, like very high, allergic levels, for example. So they have filters, like very strong filters for those specific use cases. I also really like to have tons and tons of customization options. So there's something called a housekeeping mode that will just turn on like 100 percent full blast. And it'd be very noisy. But that's assuming that no one's home, right? There's also a sleep mode, which will turn will turn the lights that turn the speeds off super low. It will still it will still continue running. But it's like sort of like, OK, everyone's sleeping. I'm going to be not as powerful at this time of night. So it was even yes. There's even a white noise option that will just like turn on at a certain level that you will turn out of the white noise to help you sleep. Some people do white noise generators. So yeah, two birds with one stone there. Oh, I mean, I'm a white noise fan on an airplane, 100 percent. So I'm really into this air purifier. It is it is a little more and more expensive. But if you get if you like how much of your life who likes data and like tech and all this like information, I do like it a lot. All right. How much are we talking about? It's like two 70 to 70. All right. All right. So it's a little less than a Mocopi. Yes. Yeah. All right. We're going to talk more about this in good day internet. But just tell us the one for the cook real quickly. Oh, yes. Sorry. This is the ANOVA net ANOVA precision cooker nano. This is the sous vide cooker.  You can make yogurt in it even you use an app.  Fantastic. Thank you, Nicole, for these. And of course, we'll have links to all of them in the show notes at daily tech news show dot com. Would you like to tell us about the advances in urinals, Sarah? Tom, I, you know, it's not every day I would say, indeed, I do. But today is that day. Scientists at the University of Waterloo have taken on a very important research project. And I'm not I'm not even being cheeky here. It's designing the optimal splash free urinal. They call the not a loom. Waterloo's Xiao Pan told new scientists, I think most of us have been a little inattentive at our post. Look down to find we were wearing speckled pants. Nobody likes having pee everywhere. So why not just create a urinal where splatter is extremely unlikely? And quote to that, I say, OK, the team presented this important research, which indeed is because who wants to have pee on their shoes? During last week's American Physical Society meeting on fluid dynamics in Indianapolis, Indiana. Pan's design encourages the optimal angle to avoid splashback, something he discovered with computer modeling, but also happens to match something you might be familiar with. That's that 30 degree angle that male dogs often achieve when they lift their legs to do their business. Pan and his team experimented, but dyed fluids, sprayed on jets, varying speeds, several distinct urinal designs made of dense epoxy covered foam to achieve their findings. The curved Nautilus shell structure of the Nautilu cut splash back almost to zero. Wow. Now, if you're saying, all right, well, what do they know? Pan is a former graduate student of Tad Truscott, a mechanical engineer who founded the splash lab at Utah State University. It was formerly at Brigham Young. That's where it is now. But back in 2018, the splash lab designed the orchid and attachment designed to I'm sorry, I just didn't want to get through this without looking designed to reduce spillage in sample collecting cups, which could lead to devices that would let perhaps people of all genders pee while standing up. Well, if you don't, if you can't pee while standing up already, I got why are you dancing around it?  I mean, I'm probably capable of it. I just have never tried. This would be making it easier, I think. Yeah. So so yeah, this is this is all good. This is all good technology for all of us. No, honestly, I mean, I know it's like, ha, ha, we're talking out pee, but this is like really cool. It's like, like just the fact that there was an American physical society meeting on fluid dynamics recently as of last week where, you know, where people talk about things like this, I think is really cool. It's important that someone is talking about it. That's what I, that's what I say. And thank you, scientists at what I would now call the Lou, the University of Waterloo. It's good stuff. It's good stuff. All right, let's check out the bell bag. Let's do it. Bill wrote in, we had a conversation about VinFast, a new EV company, newish coming out of Vietnam and making some inroads in the US. Bill writes in, the most interesting thing about VinMast to me, besides the fact that they are already shipping, is the fact that they got the design firm Penin Farina on board. That's a big deal. It explains why they're quite attractive. He means, you know, to look at them. Can't wait to see the interiors. Penin Farina designed so many really amazing cars, says Bill Ferrari, Tester Rosa, 550 Maranello, Alpha Spider, Velocce. It's a long and distinguished list of beautiful cars. I can't wait to see what they do next. Yeah, Bill, no, that makes sense. Uh, when, when you put it that way, like, oh, a Ferrari, Tester Rosa, uh, was designed by the same people who designed the VinFast electric vehicle. No wonder it looks pretty good. Yeah. Yeah, indeed. Well, thanks to everybody who writes in feedback at dailytechnewshow.com is where to send that email. And also thanks to you, Nicole Lee, uh, great gift guide and just great to see you in general. Let folks know where they can keep up with the rest of your work. Yeah. So, uh, with, um, various, uh, so you can, you can go on twitter.com slash Nicole, you can see all my, my, uh, my information there. Um, I also have a link tree, the link tree, uh, slash Nicole nerd. You can see all my different links there. I do have, uh, a blog that I'm working on, um, that will be coming soon. And, uh, I'll link them all in that little page. You'll, you'll see it when it's ready to go. Very cool. Well, we're glad to have you. We also have a brand new boss to thank that boss's name is Robert. Robert just started backing us on Patreon. Thank you, Robert. Robert is part of the, the wave. I call it, uh, uh, a boss wave because it's a wave of bosses that have been joining our Patreon at patreon.com slash DTNS. Well done, Robert. Speaking of patrons, stick around for our extended show. Good day, internet. We talk about all the things. A lot of it is DTNS and a lot of it is just food. You can catch the show live though, Monday through Friday at 4 p.m. Eastern 2100 UTC. Find out more at dailytechnewshow.com slash live. Thanks to everybody who joins us live. Always good to have you. We'll be back again doing all with Scott Johnson. Talk to you then. This show is part of the frog pants network. Get more at frogpants.com. Vitamin Club hopes you have enjoyed this program.


All right, so we're gonna start with our next talks. Our next talk is about the S-Review Video Review System, which is a video system we use at FOSDEM to review video. So please welcome the author, Wouter. Hi, thank you. So yeah, my name is Wouter Verhelst. I've been a FOSDEM staff member since 2010, and I've been involved with FOSDEM video on and off over that period. And since two years, since 2017, actually the third year now, we use a video review system here that has made our review workflow be a lot more smoother and a little better. And I'm going to try to show you how. So let me first start with a little bit of a background. Why did we do this? At FOSDEM here, we've always had video since very early on. I think 2001 or 2002 was the first year that we did video. But we never really record every room until 2014. Before then, we just did like five rooms. And then reviewing that, that's an afternoon, and after the afternoon, everything's reviewed. And you just need to transcode, and that's scriptable. 2014 was the first year we did every room at FOSDEM. Now, everybody here will know that FOSDEM is huge. We've got 24, 25, 26 rooms. It differs a bit from year to year. Now, if you have 16 hours, two days of eight hours, 16 hours per room, 25 rooms, that's all of data. That's a lot of video that you have to get the interesting parts out of. I mean, we don't want to do a lot of editing of the videos. We'd still need to have just the part that's interesting. And we don't want to see people walking in the room, people leaving the room, that kind of thing. Originally, in the first few years, only the video team would do the review. And there's like a handful of people there. They have to do it in their spare time. It takes a long time. And in 2014, the first year with every room, we were finished by September. And that was only because at that point we just gave up and we said, well, screw it. We're not going to get ready anyway. We'll just do whatever is in the database right now, and we're not going to review any further. So if you watch some of the videos from 2014, you may actually see that there's some data in there, which is like not really what you want. We did a bit better in 2015 and 2016, but that was still, in both cases, by the time we were finished by releasing all videos, most, in most cases, we actually already started to organize the next FOSDM. And obviously this was not sustainable in the long term. So in 2017, I decided to write S-Review, which is a system I'm using now. And it helped because in 2017, we were ready by late March, which is a month and a half after the event, which is a lot faster. 2018, we did a bit longer, but that was because we had a few issues that we couldn't really fix easily. And actually the majority of our talks were released two weeks after FOSDM, so a lot faster even. So that was a progress, right? So I'm not going to pretend that I invented the whole system. There were other people who wrote review systems for conferences, because we don't really have a lot of post-processing. You just need to review, check out the interesting parts, and then transcode and release. These are the three ones that I know of that are all free software. First one is a set of scripts. They're not actually named. They're scripts that hook into PentaBARF. They're very, very basic. It's just a web form. You mount some NFS thing. It assumes DV everywhere, because at that time, DV was what DeppConf was using. It runs over NFS, so you actually can only use it from the event itself because you can't do NFS over the internet unless you want to be insecure, et cetera, et cetera. So there were some issues with that. The CCC, Cares Communication Congress, they wrote their own thing called C3Tracker. It's a fairly complicated setup of Samba shares and fusive file systems, and then KDN Live to do the actual review. But the downside of the system is that it requires training of the people who are going to review. It's not a lot of training. It's only a few 10 minutes, but that doesn't scale to what we wanted to do here. What we wanted to do here is to crowd-solve the review. We're just going to save people. Here's a link, review your own talk, and come back with our review. And if you need to train people first, then that doesn't work. So I didn't want to use it. Also, very important to me in a way, at the time when I wrote Srefew, the C3Tracker was not entirely free-suffered or a few parts of it which were not free-suffered. That has been fixed since, but that was another argument for me to write something else. Finally, there's something called ViPAR. ViPAR is a review system written by Carl Karsten, who used to do a lot of the Python video stuff. I don't know if he still does that, but that's where he started. It's written in Python. It does a lot of things really well, but a few other things are not that easy to use, and it's also very difficult to configure because it's not that well documented. I can see people nodding and agreeing with me, so yeah, it's nice, but yeah, there's a bunch. So how does it work? How does Srefew work? Well, it's almost fully automated. Every bit that I can automate is automated. It assumes that a room just has a timeline of video files. There can be multiple video files. It just assumes that every video file has a start time and a length, and it just goes like, well, this starts at one o'clock and it's half an hour long. The next one starts at half past one and it's also half an hour long, so you have an hour of video, right? It knows that there's a schedule in that room, so you need to actually put the schedule into the system, and it will go like, well, we have an hour of video and I have a talk that's scheduled from 10 past one and would run for half an hour, so yeah, we have all the content for that video. And it automatically creates the first cut. That first cut, which in this example would be, will exactly be one half hour, starting from the schedule start and ending at the scheduled end. It is almost certainly wrong, but we have a first cut that's sent to the speakers and the room managers who get a link. They can see that. They can make adjustments, and after they made those adjustments, they can ask for a new cut. And the system just goes back through the first stage and does the new cut again, and then the next one is probably right because we just entered corrections. So then the speaker can say, yeah, this is good. This looks good. And then all transcoding and publishing is done fully automatic. There's some pre-roll that we do, which is like an opening credits which shows the title screen. There's a post-roll in which we show our sponsors. It also does audio normalization using a tool that is full automatic. So it makes it quite nice and it should be doable, right? Oh, right, sorry. We did do a lot of work on the user interface this year. I just did a talk at two o'clock in the open design dev room, open source design dev room, sorry. So if you're interested in how that worked, I recommend that you look at the talk when it gets released, the video, which is not there yet, but that's how that worked. How do we do it internally? Well, it's mostly a web interface. The actual transcoding and cutting and everything is done with FFMPEG. The original version that I wrote in 2017 just queried the database and then did system FFMPEG command line that had gone through shell, through interpolation, et cetera. So it was fairly basic. Right now, we've done a few things differently. I have an object-oriented interface to deal with videos, as we view videos. So you can just say, here's a video file. Tell me how long it is and then we'll just run FFPROPE in the background and give you that back. I want to create a video that's that long from that input file, so it will then just generate an FFMPEG command line that does that. And it's sufficiently abstract, I think, that it doesn't actually require FFMPEG in the backend. And I actually like it, and I'm thinking of maybe splitting off SREU video from the SREU code base itself because it could be generally useful outside of SREU as well. I actually wrote pretty much everything at least once since 2017, except for the database. The database layer was designed quite well. I expected to have to do that because in 2017, I just wanted it to work. It was a quick and dirty hack and I cleaned it up quite nicely since. It's still fairly small. It's less than 10,000 lines of code. When I checked, it was like 9,500 or something, so it's fairly, fairly small.  What is not in SREU? SREU does not have a scheduler. If you, I mean, there's lots of jobs that need to be run. You need to transcode things. You need to upload things. So we've got one master host and a few hosts that run jobs. We don't actually schedule that. I have been doing some work in high performance computing and I just used one of those tools to schedule jobs on all the systems. Grid Engine in my case, but it doesn't require Grid Engine. You can use any DRM system. So that's actually a major difference between the C3 Thacker and Viper. C3 Thacker is mainly a scheduler and the review part is just while we used KDN live, so they didn't implement it. Whereas in my case, it's pretty much the opposite. Viper has a fairly important scheduler part too, although you can work around it as different. There's also a few things that are not in the code yet that I do want to add. The administrator interface currently is fairly basic because I haven't gotten around to making it well yet. So that's something I want to deal with. Right now, if you create an output profile, so you can tell SQQ, I want a WebM and an MP4 and an AV1 version of this video and it will then transcode them one after the other. So my plan is to also make that happen in parallel so that it will upload a version as soon as it's ready. The database abstraction, we have been starting work on that, but it would be the intent to work on that a bit more. Also, there should be an RPC sub-system which is related to that. Right now, every script just accesses database directly and I want to do some XMRPC or JSON or whatever, something like that. And well, I actually found some bugs when I was dealing with it right here, so fixing those would be nice to ensure. That's pretty much it. Actually, I thought I had more slides. I can maybe do a little bit of a show how it works. Let me open this. Where's that browser? Oh, yeah, that helps. Oh, there we go. So this is the overview system of how SQ itself. We have things here. Those are all the talks that it knows about. There are many talks because Fosname is a large event. We have an overview at the bottom. So basically, every talk is in a particular state in the system. Waiting for files means we're still waiting for content. Cutting means while that part is currently going through a catch that we were extracting just in content. These are waiting for people to review. Well, it shows there. Five of them are currently transcoding. One of them has already been released which is the opening talk of this morning. These are where people entered something in review saying, well, can somebody please look at this because I think it doesn't work. So I'll have to go in there. And this is because my colleagues of the video team made a mistake and I have to keep those in hold for today. We'll fix that today. The final one, ignored, is because there is no data for the key signing. And obviously, we don't release a video for that which would be very boring. So that's why that one is ignored. But the schedule is important automatically from the website. So if I remove it, it would be back the next time the schedule runs. So that's why we just said, do ignore it and then we didn't see that. I think I can. No, I can't. I was going to show you the review interface but the interface requires a link that has 64 random characters and I'm not gonna type 64 random connectors on my phone. So that's not happening. Any questions? Go ahead. Yeah, wait for the microphone please. Sorry? Have you considered any sort of physical button for start and end of talk inserting cue markers into the stream so that at a minimum, there's a copy that can go up that is at least trimmed? So Viper does actually have support for that and it's not necessarily a bad idea. The problem is, let's say, I say thank you and then everybody starts clapping and somebody pushes the button and then somebody goes, hang on, but I have a question. You've got a marker on the wrong location. So you will need to have that review anyway. And for that reason, I don't think there's much of an advantage because it will confuse you because or the person who was pushing the button pushes it like three times so which one is the right one now, right? So it's not a bad idea per se but it won't be good enough. You will need to review anyway. So in that respect, I was like, let's not go there. But was there something else to say? No, yeah, it could be useful but not really. Yeah, well, that too, exactly. Anyone else? Other questions? I ran through my slides, I guess. Although, what we could do is that I couldn't check my mail in. Yeah, that's a good idea. And now you can watch, yeah, that we can do. Just leave me. We can do a live review here. Sure, sure. So all the review requests are sent to the speaker as well as the deaf room responsible and since he is a deaf room responsible. Yeah, that's cool. That's good enough. Maybe make it look good again on the. Yes. Something's working on it, making noise. There we go. Okay, I think it's good. This is not what we want. That's not. That is not what I want. You've got the control video. I think the external screen is not on the mirror right now. Oh, shoot. Sorry. Oh, no worries. There we go, there we go. So basically, it shows you what video we're reviewing and it gives a little bit of instruction on what to do. If you scroll down a bit for me. So this is the video, you can watch it and then if you go like, something's wrong with it, then we select the bottom option. Can you do that for me? The video has problems. So yeah. That one. Yeah, no worries. There we go. And now we can select, well, it's too early that it starts or it starts too late or we have previews of the audio channels because the microphones over here, like the lapel mic is going through a mixer and is going with XLR into the camera. But we also use the on camera microphone as a backup which goes to the other channel. So we actually have two channels. And then if something is wrong with my lapel micro or whatever, then the speak and at least select the in camera microphone as a backup. And the third one is both mixed together. Yeah, yeah, yeah. We used to have some AV sync issues in past year. So then we can fix that up as well. And if that's not good enough, then people can enter some explanation here. And then the talk, it's marked as broken. It's a really basic interface. It's a hand holding interface. It's much easier to use this time around than it was last year. So if you were a speaker at Folsom last year, you probably won't recognize this. But it's exactly the same thing. And the backend is just scripts calling it, right back. Yeah, okay. Stereo, wow. So does fiddling with this, if you say here's the other channel, does that actually reprocess that? Or is this just send a message to somebody with a clue? No, no.  You'll need to take a bit of this and a bit of that. All of the form up there is processed automatically by the system. So every change you enter there will be used. If you enter something here free from there, then somebody who has a clue will have to log in and check and see what's happening. In most cases, we'll have to say, well, sorry, we can't help you then. Or we can say, well, here's access to the raw data if you want to just go ahead and I'll inject it into the system. That works too. We do that occasionally. So someone could get access to all the raw streams if they needed to like, if you had to drop out for part of the talk, so you had to use this bit and then you could flip the other one and then put it back in. Like now you need to do some video editing. Right, right. Is there a way of that? Well, we don't actually throw the data away. It's on the server. Some of it is on SD backups, et cetera, et cetera. So there is an option to do that. It's not more work and we won't do it. But if a speaker says, I want to invest the time, then we'll go, yeah, sure, here's the files and have fun with it, right? And then when they give it back to us, we'll upload it into the system and then publish it as well. But other than that, we don't actually, we don't do much of that. Any other question? We still have five minutes to go. This is good. No? We have one minute and 10 seconds left. So. Are you doing lots of reviews for POSTA next year? Do you want me? I hope to be here next year. I don't know yet. Andy knows that I'm moving to Cape Town in a week or so. Okay, so thank you. Welcome. Presenting.