Okay, I think I can start now, so are there any questions from last time? Okay, let me try to remind you, basically the plan of my lectures was that, first lecture was quantum mechanics, second lecture was about today is going to be about quantum field theory, quantum fields, third lecture will be about general relativity and classical black holes, and the fourth lecture is going to be about quantum black holes. See, it's a very steep, I don't know how much we will succeed, but actually we more or less succeeded in explaining quantum mechanics. Today I will explain what are quantum fields. And the objective is, as I said for this book, I want to explain the connections between various aspects of quantum black holes and topics in number theory and geometry, in a manner that should be accessible to any mathematician or a student from other areas of physics, with a rudimentary knowledge of the basic undergraduate physics that they may have seen. And with that view, we started to develop a dictionary so that we can communicate with each other. So, we said that a physical system S, with it we associated a Hilbert space, then we said that the state of the physical system, we associated with it a state vector in the Hilbert space. And in fact, as there was already mentioned, physically what is, it's really a ray because the vector and another vector multiplied by a phase have the same physical consequences. So, you can, you have to keep this in mind, so it's really strictly speaking a ray, that in a second. In this notation, it's only a phase and the norm can be anything. No, notation does not imply that it's e to the i theta, where theta is real. No, no, so this can be any real number at this stage. I don't want that, so I will come to that. Yes, I mean, we will come to that, I will mention, I will come to that, yeah. Yeah, we are jumping ahead. A physical observable, yeah, I will try to, I mean, there have been some of these confusions, so I will try to address them so that they are not important confusions, but it can stop you from, so we said that these are self-adjoint operators like A, for example. And the eigenvalues, results of a measurement correspond to the eigenvalues of the operator. Sorry, alpha, let's say, alpha i of the operator. So, if you perform, if you measure some observable given a state, the result that you will obtain will be one of these eigenvalues of the observable alpha. And the probability for if, and let's say P i is a projector. So, this is the measurement axiom which I didn't really explain in detail last time, because that was a bit of a diversion from what I wanted to do, but let me state it anyways. If P i is a projector onto the eigen subspace of alpha i, the probability given a state psi, the probability of obtaining the result alpha i, if you have identically prepared systems, is given by psi P i psi divided by psi psi in measuring. Okay, very good. We introduced, we discussed a very simple system which is the harmonic oscillator system. So, there was a Hamiltonian, another concept was Hamiltonian, which was a self-adjoint operator, which was responsible for the time evolution. The time evolution of the state was given by unitary evolution. And one particularly simple Hamiltonian that we considered, this is called the harmonic, the quantum oscillator, I called it. And the Hilbert space, in this case, was a Fox space representation. Simply given by, it's like a highest weight or lowest weight representation, built upon a Fox vacuum, a set of states a dagger 1, etc. a dagger to the power n, the root of n factorial. So, I'm now going to choose a psi which is normalized to 1, to give an orthonormal basis for this. This is state 1, the state n. The set of vectors n furnish a basis, furnish a basis for the Hilbert space. Now, from here to make a transition to quantum field is actually relatively easy. That's what we are going to do. Intuitive idea is that if you have like an electromagnetic field, a classical field, it's Fourier modes, if you do the harmonic analysis, then the Fourier modes behave like quantum oscillators, oscillators for a classical field. And then by regarding those oscillators as quantum oscillators, you basically get from it a quantum field. And I will explain how that happens for a simple example. Let me erase this now because I want to write the dictionary here. So, before getting into quantum field, let me try to explain what is a classical field and classical fields.  Let me explain that a little bit. So, all physical processes take place in space and time. And if you have a d-dimensional space, then locally like in this room, you can select coordinates xi, xm. Let's say m goes from 1 to d. The event, any event in space time like I throw the chop up, this event is specified by or a light flickers is specified by its location. So, some space coordinate and then some time coordinate. For Newton, at Newton's time, time was absolute. What that means is that observers in relative motion record the same time. So, my time and the time of the person who is in a train is the same. So, if I have two observers using two different coordinate frames, then you will have xm prime, but the time will always be the same. If I have an observer O prime and observer O, only the space coordinate was changing and the time was absolute. And the essential insight underlying Einstein's relativity is that time is relative. That's why the name relativity, which means that time also can change. Depending on the time recorded by the person in a train doesn't have time of one particular event or the distance between two. If you have two events and they're separated by some time t1 and t2, here their time would be t1 prime and t2 prime. And they can be complicated functions of this coordinate. So, therefore that the fact that time is relative means that you should really not regard space and time separate with space time as a together as a single entity. And in fact, in spatial relativity space time is just, so in general it's a single entity and it's going to be a Riemannian manifold, a manifold. So locally and it's going to be a pseudo Riemannian manifold.  So, what that means is that in the simplest case, it's going to be generalization of R1 plus D, which is a Euclidean flat space. We'll go over to R1, D, flat space and this is called the Minkowski space time. Here the metric, there is a metric tensor you can write down. Here it will be just 1, 1, 1 diagonal for Euclidean space. Whereas here the metric is delta mu nu is the metric. Here the metric has 1 minus sign. The only difference between spatial relativity and Euclidean space. Minkowski space time and Euclidean space time differ only by this very crucial minus sign. Which means that the line element here is just dx mu square dx mu dx nu delta mu nu summed over mu nu. Whereas here it is eta mu nu dx mu dx nu. When in particular dt square, sorry, ds square is going to be minus dt square plus dx vectors. So, x vector is just the space vector. Euclidean Riemannian manifold you define as something which locally looks like flat space. You have a chart and then you locally it's flat. Locally you can have a chart, a map onto. So, basically you have a local chart Minkowski. The pseudo Riemannian manifold is a manifold in the usual sense with a chart. But the metric is not Riemannian, it is not positive definite. It has a signature minus 1 minus and d pluses. The pseudo Riemannian manifold simply means that the metric of signature. Given such a manifold you can consider various things like a tangent bundle on it. Let's say a tangent space at any given point is a tangent space T of m or T star of m. So, given a manifold you can consider various bundles. If you think of it as a, the structure group, I mean if you think of this as a vector here. If you have a metric pseudo Riemannian metric just like, just this is a complete analogy between the Euclidean manifold and the pseudo Riemannian manifold. Riemannian manifold and the pseudo Riemannian manifold. Just that you replace a positive definite metric with a metric with a minus 1 minus sign. This is a metric g mu nu. So, this, the structure group, it's called a structure group right. It's acting here is instead of being SO d plus 1 is SO 1 comma d.   I think everybody, all mathematicians are usually familiar with Riemannian manifolds. And on that you can define tangent space and cotangent space and various bundles right. You can take symmetric product. So, a classical field in general is a section of some bundle. And depending on what bundle you choose, you call it a scalar field or a spinner field or a vector field or a metric field. Okay, so that's the definition of a classical field. Is this clear? Let me take a simplest example of scalar field. That's just a function phi of x. I will use x to denote all the, all these coordinates. So, x will really mean x mu. And when I put a vector on top of that, it really means x m. This is going from 0 to d. This is going from 1 to d. In fact, you can have more general bundles. You can have some other compact group. And you can consider, for example, the principle bundle. Spells principle. And the sections of this are the g, the sections of this bundle also you can consider. And these are called gauge fields. So, you can consider associated bundles in some representation of this group. So, you have basically a, your total group is spin one comma d cross g. And so locally, you have some chart in this manifold m. And the fiber is some representation of spin one comma d and a representation of this. So, let's call this representation r. And this representation r tilde. And if, for example, if you have a explicit vector space representation with some index a and here, here's some index alpha, then a classical field is simply some object with two indices as a function of x, which is a section of this bundle. In fact, the simplest group to consider is g is equal to u1. And if you take a u1 bundle and you define its connection a, then in some local patch, you can write it as a is equal to a mu dx mu. It's a one form. And physicists would call this a mu. It's clearly a vector, a contra variant vector field or a form. It's really a form. They will call, this is known as the electromagnetic potential. No, no. This is a connection of the u1 bundle. So, in other words, you can define a covariant derivative delta is the connection. It's the u1 connection. It's the gauge field of the group. So the electromagnetic potential is basically a gauge field in this definition of u1. This is local. It's in the local. No, so in many situations where it was encountered, the bundle was trivial. So it's a bit pedantic to call it a bundle. For example, if you just take the flat Minkowski space, then the bundle is trivial. But there are situations where the bundle is non-trivial. So, yeah, so therefore, yeah. Sorry, it's a connection. It's a connection. Sorry. I'm sorry. Did I say it wrong? Sorry. Connection. I'm very sorry. Yeah. E is a connection. Other fields, you can have an associated bundle. So you can have other fields can be sections of associated bundles like a scalar field. Suppose you have a scalar field, now what is the connection? Connection. So how do you want to say it? Okay. Sorry. Yeah. Let's say a connection one form corresponds to a gauge field. Does that satisfy you? So for example, here we took a scalar field, but that scalar field could have been, if you had, for example, representation of some group with, let's say, SUN, group like SUN, then Phi could be in the fundamental representation. It could have some additional index. Same thing. I'm just saying that if you encounter these, don't get scared because their physicists use different words. They call it a electromagnetic potential. Some people will call it a U1 gauge field. Or if it's U1, in general, it could be an SU3 gauge field. Surprisingly, in physics, G is equal to SU3 cross, SU2 cross U1 is all that you require to explain essentially all the physics that we have encountered thus far in the, up to the Large Hadron Collider. It's quite a remarkable fact. It's kind of, from a mathematical point of view, it's not clear what is so special about these groups. But from a physical point of view, they are special. And this is related to the strong nuclear force. This is the electromagnetic force. So, these together, in fact, the ICTP were unified by Salaman, which is basically electromagnetism plus weak nuclear force. No, no, no. Not at all. So, in fact, that's, I'm coming to that point. These are classical fields, but they satisfy classical equations of motion. And this is how I'm going to make contact with our previous discussion where I'd considered Heisenberg, Hamiltonian equations of motion. The classical equations of motion are simply some partial differential equations satisfied by the classical fields. The connection is not flat, but it must satisfy a classical partial differential equation. So, it's not any field, but physically relevant fields must satisfy these classical equations of motion. And there is a quantum version of that which we will come to. And that's what we'll make contact with our harmonic oscillators and this discussion, which so far is perhaps a bit abstract. So, let's take the simplest example. If you have a U1 gauge connection, A, it's a connection one form. I can define from it its curvature two form, the curvature two form. It obviously satisfies the Bianca identity. And the equation of motion is D star of F is equal to 0. So, these are some very simple generalizations of basically partial differential equation generalizing Laplace equation. For example, if you have a scalar field phi, it just satisfies D dagger D, I mean D star D plus D star D star, I mean D dagger. You can define a dagger operator which is, ok, but star is the hot star operation. So, in particular for a scalar field, this is nothing but the scalar Laplacian. So, I can call it delta phi equal to 0, delta phi is equal to scalar Laplacian. Delta is equal to scalar Laplacian. It's actually not a Laplacian because it would have been a Laplacian if it was Euclidean with that 1 minus sign, it is called Dalyan version, but ok, you can think of it as a scalar field, a classical scalar field in D dimensions, D plus 1 I mean dimensions because 1 is time satisfies delta Laplacian acting on phi is equal to 0. There can be more generalizations of this. For example, it can be delta phi is equal to m square minus m square phi is equal to 0. Notice that this is still, let me write it like that. My convention maybe there is a plus here. Notice that this is still a linear equation, ok. The sign is important because that actually will determine whether that particle is tachyonic or massive. So, the sign is important. We can figure it out actually. So, this operator is del square delta square. So, it is going to be E square minus P square minus m square. So, this is correct. This sign is correct in my convention, ok. But more generally you can also consider slightly more complicated nonlinear equations. Now, if I choose a coordinate frame and this can be in many dimensions, it can be in four dimensions, one 3 plus 1 dimensions. So, the particularly interesting manifolds of our interest are going to be, of course, we live in four dimensions. So, 1 comma 3 is a very special one. It is going to be what we will be talking about mostly. It can also be R 1 comma 3 if you are in Flatminkowski. Or it can be m 1 comma 9 which is what is required in string theory. Or you could consider m 1 comma 1. For example, I will do it. You can consider any possibility, right? You can consider R 1 comma 1. Or you can consider m 1 comma 9 which is of a special form. R 1 comma 3 cross some 6 manifold. And again in string theory, this 6 manifold is often taken to be a Calabi or 3-fold. In a complex 3-fold. So, with this description, so let me actually take a pause here. So, last time we described quantum mechanics. You know just single harmonic oscillator, Hamiltonian, Hilbert space, a state, etc., etc. We slowly want to make a transition to quantum field theory. We did the part, quantum part last time. Now you want to go to the field part. And eventually we want to go to general relativity. Here is this and make it a bit neater. We had observables, self-adjoint operators. Then we had space time as we said is a manifold m 1 comma d. And fields, they can be either connection forms or they can be curvature two forms. That is also a field because it is defined at every point or sections of various bundles. And now I want to explain what is a quantum field. And it is one way to say that it is kind of operator value distribution. To begin with, you can think of it as a function. But for some other niceties you require it to be distribution to make it more. The notion of a classical field you understand. I mean I hope it is clear. The phi of x is a scalar valued function. A scalar valued map from m. That is the classical field. And we are going to make it an operator valued map. In general, I am just taking one example of a quantum field where it is a scalar valued map to begin with. A classical field which is a scalar valued function to begin with. If you have a connection form, then you will have a vector valued quantum field and so on. For the metric, as we will... Let us not go there. Because we actually don't really know how to associate a quantum field with a metric completely. So I think between classical field and quantum fields for us is going to be through these equations of motion. And to do this, I am just going to illustrate this first in the simplest example. Namely, I will take a scalar field. And this is actually an important example because t and x in r1, 1. So not r1, 1 with a further identification. So the classical field satisfies a simple equation delta phi equal to 0. The plushian in 1 plus 1 dimension is particularly simple because it is just minus del square in r plus del square del x square. And if I write t plus x is equal to x plus and t minus x is equal to x minus, then this becomes minus del plus del minus 2 times maybe. This is exact analog of if you had a plushian with a positive sign. Let us say del x square del y square plus del square del y square del x square. This will be just del z, del z bar on a complex plane.  And here it is del plus del minus. So we have an equation del plus del minus phi is equal to 0. Now remember last time we and I want to now get a quantum field. I want to now introduce a quantum field based on what we discussed last time. So last time we discussed consider harmonic oscillators, quantum oscillators with frequencies infinite number of them omega r is equal to just r. Frequences are basically 1, 2, 3, 4 like that. The Hamiltonian is just going to be omega r, a r dagger a r summed over from r is equal to 1 to infinity plus a half. I have an infinite selection of operators a r and a r daggers. I can also consider an identical system with a tilde in the same property a r tilde dagger a r plus half. I have another set of operators a r tilde a r tilde dagger. Recall that a r and a r dagger satisfy the Heisenberg equations. Just a and a dagger if you remember last time we had equations. That I da by dt is equal to minus h a and so on. And more generally I d of any operator a in this theory is defined by particular we last time we defined operators we can write a is equal to some q plus i p with some scaling that we had written and q and p also satisfied. So q also satisfied this equation and the Hamiltonian was q square upon 2 plus sorry omega square q square upon 2 plus p square upon 2. So now I am just going to construct the following operator. Phi of tx left moving I am going to call it. You find this is just a definition as a r e to the minus r t minus x plus a r dagger e to the plus i r. So it is a real field and I can define the right moving field.  I hope I have not lost everybody by this time. Let me recapitulate. So this system we understand very well harmonic oscillators. I will now just take a collection of harmonic oscillators. This is nothing that is as simple. They are completely I just Hilbert space is the product of those Hilbert spaces. Hamiltonian is the sum of the individual Hamiltonian. And I just declare this to be my, this is clearly an operator valued field because it is a map from space to an operator, right? That is what is meant by an operator valued function or distribution. And now I am going to call phi of t x is equal to phi of left t x t minus sorry this really depends on t minus x and this depends on t plus x. Why do I do this? It will become clear to you in a moment. By construction del minus del plus phi is equal to 0 because you see the quantum field satisfies the Laplace equation or the Lahrenberg equation. Moreover, you can define an operator phi which is the derivative of phi d phi by dt which is an exact all of this p. Here if you found, if you look at the equations of motion of p because the Hamiltonian is really just p square upon 2 and the commutation relations of q and p is i. This is the famous Heisenberg commutation relations. p was simply dq by dt. And this is called sometimes the conjugate momentum. Then the Hamiltonian has a very nice property that we wrote down r, ar dagger, ar. The total Hamiltonian is this, right? The left Hamiltonian plus the right Hamiltonian is equal to an integral 0 to 2 pi over x. i is also filled as a function of t and x. It can be written as d phi by dt whole square, I mean del phi by del t plus del phi by del x whole square. And in fact, this is pi, so this is pi square. If I replace pi then it becomes d phi by dt, sorry, partial. Now, this might look a bit complicated but it is not complicated. The point is the following. If I just take this definition of the field, take its derivative and then do Fourier transformations. Then what is going to happen is that the integral over x will basically make sure that the r of this and r, they are coupled together. They will enforce a delta function. And that's how you can go from here to there. So, this is an exercise that take this expression, substitute this into this expression, do the x integral and you will get this. It's a straightforward high school exercise. Now, we come to the important point is that this Hamiltonian is a local density. This implies that the Hamiltonian is an integral of a local density over space. So, let me give you some picture about this. Your manifold is this. Now, this is really r, it's really s1 cross r. This is your time coordinate and your x coordinate is periodic. And you have a field defined on it which is t as a function of x. If you did Fourier analysis along the x direction, what you will get are modes of the field oscillating around with different frequencies. And that explains why the frequencies come out to be integers because they all have periodicity 2 pi, a fixed periodicity. So, to begin with a priori when we just thought about harmonic oscillators, these frequencies had no reason to be integers. They could have been any frequencies. But here in some unit, because this length could have been 2 pi L for example, but the important point is that r is r upon L in that case and they are integers based. We have taken L to be 1, but we'll shortly consider the more general case. So, the important point is that the classical field when you... So, therefore the quantum field, this is the slogan that I had told you, is simply a collection of harmonic oscillators, quantum oscillators. Okay, I think this time I perhaps lost more of the audience. So, maybe I should stop and ask questions, wait for questions. This is a special case of a manifold, right? I'm going to consider more general manifolds later on. Yeah, the point is that the quantum field is well defined even on a curved manifold, but it's much more complicated to describe it. But it can be described, it's done now. It's pretty well understood quantization of quantum fields and curved space then. We will do that because that's what leads to Hawking radiation. I wanted to avoid talking about Lagrangians because it becomes a whole lecture on in itself. And I wanted to take the shortest path to... Another way to do it is using Lagrangian mechanics and actions and that's more naturally suited for path integrals but which are usually harder to explain to a mathematics audience. Yeah, I reversed the order because I... It's again because I think quantum field, I can define it in this manner. You're right that normally one starts with a classical field and does something called quantization. But the quantization is not really... One can always take a classical limit, but going from the classical to quantum is a bit of a... It requires some physics and I wanted to avoid that discussion. That's a good question. Yes, absolutely. Absolutely. If you want to include interactions, basically they are oscillators with unharmonic interactions. So you can also view them as oscillators interacting with each other. Yes, yes, I agree with you. But I will come to interactions shortly because first I want to explain what is the meaning of a particle and what is the meaning of a state and so on. Exactly identical thing exists. It's a lot more complicated to describe it, but quantization of... You can quantize all connections. Quantization of connection, one form has been done. That is known as quantum gauge theory. And that procedure is much more complicated than I want to get into. It's not going to be required for our purposes, but it exists. Yeah, so modular space is a much smaller subspace of the space of all fields. Here we are considering a much bigger space, which is the space of all fields. An equation of motion, but that's much larger than the modular space, generically. In some cases the space can be simple or flat connections. Yeah, but that's actually a good point. In many cases you can quantize that space and that's a simpler version of... So in mathematics literature this appears like a space of flat connections. Those are special cases of this. Okay, let me just recapitulate. The point is the following. A classical field satisfies some equation like Laplacian of phi equal to 0. We constructed an object while the quantum field which satisfies the same equation. So quantum field satisfies the same equation. That equation can be viewed as a Hamiltonian equation of motion because if I write it's basically d phi by dt, you can check it's the same as minus h phi and i d phi by dt that I defined is minus h phi. And if I, using this equation which will turn out to be exactly the same as phi dot, i times phi dot, so if I replace phi in favor of phi dot, I will recover this equation. So the equation of motion satisfied by a quantum field, this was the statement that I wanted to... Sorry, so with the replacement phi is equal to phi d phi by dt. Because there was an i here. Sorry, sorry, what am I saying? With phi, sorry, sorry, sorry. Phi is equal to here. From here I will get i d phi by dt is equal to i phi. So with one of the equations of motion will simply tell you phi is equal to d phi by dt. And if you replace phi everywhere, then you will recover this equation. So see Heisenberg equation of motion are for two objects phi and phi. But that's just a way of writing the second order differential equation in terms of first order differential equations. By introducing phi is equal to d phi by dt. You can always write the second order differential equation in terms of first order differential equation if you double the number of variables. That's basically how the phase space was introduced. If I just define phi is equal to d phi by dt, this equation can be written as a first order differential equation. And that first order differential equation is the same as the Heisenberg equation of motion. The final thing is that the Hamiltonian is local. Meaning it's defined by, depends only on derivatives. It doesn't depend, it's a local meaning that it's an integral of a local density. And that local density can be constructed using just derivatives, local quantities. If you look at it, it involves the derivative with respect to time and it involves derivative with respect to x at the same point. So that is the notion of locality. Now this is really very crucial. This is a very important concept because locality is very closely tied to causality. And it has this, right? Let's see. Yeah, I can, it has this. The Hamiltonian does not include terms like this. Phi x times some kernel. It could have had terms like that, right? This would be non-local because you will require the value of the field here and the value of the field in Andromeda Galaxy. Then you'll have to do something, take an integral of them and this is not local. This is bi-local. You could call it bi-local if you want. But it's really not local. And this is really fundamental to quantum field theory. That the light, the signal doesn't propagate instantly. Causality means that first of all, the cause precedes effect and signals do not propagate faster than the speed of light. You cannot communicate. Okay, let me contrast this with Newton's law of gravity. If you remember, Newton's law of gravity is that the force between the sun and the earth is the mass of the sun times the mass of the earth divided by the distance between them. This is not local in time. It's instantaneous in time. Because suppose the sun disappeared tomorrow, then you will suddenly have to put this force to zero immediately. But you know that the light takes eight minutes to come here. And this actually bothered Newton a lot. I mean, you think that Newton just wrote it down, but Newton, there is a letter by Newton saying that this sounds totally bizarre. This cannot be true. And this is really critical for general theory of relativity. And you probably heard about the gravitational wave detection recently. That has to do with the fact that something happened, the black holes too, black holes merged. But that signal took billions of years to come here, one billion years to come here. And we detected them today. But the event actually took place long time ago. This kind of thing cannot happen in quantum field theory. So Newtonian gravity is not allowed according to our principles of local field theory. And that's why Einstein had to construct his theory of gravity, which is local. Now I'm going to connect it to modular form so that you can appreciate some of these things a little bit better. So you remember we introduced a partition function.  But q can be e to the 2 pi i tau. And let's just take the left moving. You remember the Hamiltonian was the left moving Hamiltonian plus the right moving Hamiltonian. And so h left was just with r, e, r dagger, e, r. I'm going to ignore the tildas. There was a similar expression with the tildas. And this we evaluated. Now notice here, it is an infinite constant. And let me call that the energy of the Fock vacuum, the ground state energy. Because now we have a collection of infinite number of oscillators, there is no guarantee that things will be finite. And here is a simple example, that even though this half is a finite, after you sum over infinite number of oscillators, there is a potential for divergences. So let's keep this energy e naught. This is the energy of the, because that's the Hamiltonian, eigenvalue of the Hamiltonian for the Fock vacuum, which by definition is the energy of the Fock vacuum. So h acting on the Fock vacuum is equal to e0 times the Fock.  So this is going to be e to the e naught, q to the e naught. That's, we don't know what to do with it. And this leads us, but we said, aha, sum over r, zeta function regularization, that I will regularize e0 s to be half sum over r to the minus s, where s is not equal to, sorry, s is not equal to 1, sorry, s is not equal to minus 1. When s is finite, I can evaluate this. Then I will, so this is, looks like a bit of cheating, but let's do that anyways. That will give us minus 1 upon 25. I agree, zeta of minus 1. Yeah, we have to do an analytic continuation, there is a pole, so it's not, there is no pole at s is equal to minus 1, sorry. Now this looks a bit ad hoc, but the point is that this is one of the examples of what is known as renormalization theory in physics, in quantum field theory. I want to take this as an example so that, of course the renormalization theory is a very vast subject, and part of the Princeton notes were actually trying to, really try to define it in some more complicated way, I mean in the more detailed way, and that is much more complicated than what I'm describing here, but it should, I wanted to give you a flavor of it so that you should understand what it means, and it's not something, I mean after all Euler also did this, so it's not something that only physicists do without any reason. And one of the, let's try to understand it a bit more physically, why we did the zeta function regularization. So one can use a different regularization, and the problem is the following, that we have, our space is like that, think of it as like a violin string, of course the violin string is, has a Dirichlet boundary condition, so the violin string has modes, Fourier modes which are like that, and those are the different integer-valued frequencies. Here we have periodic boundary conditions, so again we have integer-valued frequencies, but of course we know that the violin string cannot oscillate. Once it hits the atomic size, there is no sense in whether, you cannot really take the frequencies of the violin string to be extremely high. Very high octaves of the violin string don't really make sense. So that suggests that we should perhaps, sorry did I bring my notes or not, I forgot my notes. I'll have to do this by memory, which is not a good idea, okay but I hope I don't make a mistake. So you can regularize it differently, so what this is doing is that, it is really cutting off, and this you can do very explicitly, and clearly as epsilon goes to zero, the pole here, as epsilon goes to zero, there is a, in fact when you take a derivative, there will be a double pole, and this again I leave as a homo exercise, because I didn't bring my notes, but we can even do it here. Can I leave this as a homework exercise? You can take this function, and expand it in powers of epsilon. What you will discover is that it has a pole minus one upon half epsilon square, minus one upon 24, plus order epsilon. Notice that there is no term of order epsilon, one upon epsilon, some number times. Now notice that our violin string was, had length 2 pi, but actually it could have had length 2 pi l, and the atomic distance scale was say a, then epsilon which is a dimensionless parameter is really a divided by l. A is another cutoff, so a is the distance, is the atomic distance. A is, if the violin string had length l, then I can define, I'm trying to explain the physical origin of this cutoff. Physical origin of this cutoff is that, very high violin frequencies are getting cutoff, and at what scale does that happen? At the scale where the atomic distance is important. So if the total string, violin string is of length l, you are introducing a cutoff epsilon, which you can take it to be purely mathematical cutoff. But you can imagine it also is coming from this following physical cutoff that the violin string actually has, beyond that point, it doesn't really make sense to think of the violin as a violin string as being a long string, but it's really composed of, because it renders, no, it's a cutoff because basically, R, which is much bigger than one upon epsilon, does not contribute to this sound, right? This is a smooth cutoff. Yeah, it's a smooth cutoff. It's called a cutoff. Okay, let's not argue about it. Okay, but it's a matter of terminology. In physics literature, it is called a cutoff, and it's a smooth cutoff. So you can call it a smooth cutoff, and that will make you happy. But it's a cutoff in the sense that higher frequencies of the violin string are cutoff, meaning they are contributing less and less, exponentially cutoff from there. So it's true that it's not a sharp cutoff, but they're exponentially damped the contribution to this interval. Okay, and that typical, the frequency that you will hear the most, I mean the maximum frequency that you can hear is of the order of one upon epsilon, right? Energy E0, in that case, if you had length L, between one upon L times half R, because the frequencies were one upon L. If I now, if you look at the term which is, this goes as one upon L times epsilon, which is epsilon square, some constant times epsilon square minus one upon 24. So this goes as E square, if you plug it in here, this expression, A square times L minus one upon 24, divided by L. It is going to zero, I mean A upon L is going to zero, right? Now here you see the locality, because you see this quantity can be viewed as an integral over, so the renormalization procedure, no, I have not left the, for now, just give me two minutes to, I will come back to the world of mathematics. Just be patient. If I define epsilon is equal to A upon L, this is a completely mathematical statement, right? What are you not satisfied about? If I substitute epsilon is equal to A upon L, right? That follows? Okay. The point is that this is proportional to the length of the string. And I told you Hamiltonian is a local density. And renormalization is a procedure, says that because we are dealing with infinite number of oscillators, right? And the procedure is twofold. One is called regularization, which is a bit like what Euler did. You know, you can make it a zeta function regularization. So zeta function, you can use the epsilon regularization, et cetera. So the point is that you have infinite number of oscillators, and that's what is causing the divergence in this case.  You basically make sure that not all of them contribute to your problem. Or the ones that contribute, you put a smooth cutoff. You can also put a cutoff. I mean, the kind of sharp cutoff that you want can also be used. And that is another way to do so, yeah. The second step is renormalization. What does renormalization mean? Renormalization means that you're allowed to add local counter terms. Actually, all this is much better stated in the Lagrangian formulation. Since I didn't use it, maybe you should keep it in the back of your mind. The whole thing is much nicer to do it in the Lagrangian formulation. I'm just doing it in Hamiltonian formulation for the sake of economy because otherwise. What does it mean? The point is the following, that if I'm considering the Hamiltonian of a Hawaiian string, how do I know that the energy is really what I wrote down? There could have been an overall constant that I could have added, right? Hamiltonian was some density local density, but surely a number like a square is also local density. It's an appropriate sign with a minus sign. Minus C over, there was some C here, no? If the C is half, then it's half. The point is that that half is unimportant for physics because I can remove it by adding a local counter term. But I cannot remove this. You see, 1 upon L, I cannot remove by adding a local counter term. Looks confusing. No, no, so the point is, let me explain what I mean is that the rules is that by allowed to add local counter interrupts to the Hamiltonian, let me finish the sentence then it will become clear to remove the divergences in the regularize a going to 0. Adjust the coefficient in precisely such a way you can get rid of this divergence. It is local and it... No. So the point is that in this example there is a local counter term allowed. This quantity is local, you agree with me? Yes, this is the first term. Show us the first term. That also actually, in this case it turns out that your question is certainly valid. In more generally, there will be more general local counter terms allowed. There are rules. If you take a more general Hamiltonian, this Hamiltonian plus say, let's we add another term like lambda 5 to the 4. In this case, actually, you are allowed to add more local counter terms which can be proportional to this and also the counter term that you were talking about which is proportional to this. That's what I want to say because this is a low energy physics fix but let's say how I want to state this for a free case. So to remove the divergence and the limit keeping low energy physics the same. So the point is that that's one way to say that. You have some frequencies which were 1 upon 2 pi 1 and 2. We cut out some very high frequency modes which were very high frequency which was the limit in physical situations is taken in such a way that the physics at low energies does not change. Now you can ask does this not change the physics but actually what you measure what you are able to measure are only differences between this is actually a particularly bad example of renormalization because this is the famous cosmological constant problem which you cannot measure without having gravity but it's clear that what is physically important is just differences in energy because the overall origin of where you put the energy actually has no meaning. So therefore this counter term is allowed. If you do what you do of course you will get rid of the whole thing. So you want to keep the physics at low energies fixed. I would have said that except that that's not correct. Because 1 over L is not local if L is the length of the universe you want to have a quantity which does not depend on that. If I change the length of the universe I should not change the local physics based on the length of the universe. So you don't want to add something that is the meaning of locality that if I added something which depends on the length of the universe then it's clearly not local because in this example perhaps what you said is the best way to say that so let me make the correct statement you can actually add terms dependent on 5 square so that's why I didn't want to say it the way you stated it but let me state it more correctly So in a quantum field theory generically you will get divergences because you are dealing with harmonic oscillators of infinite harmonic oscillators but you can always regularize it using the smooth regularization procedure if you don't like a cutoff, smooth regulator let's use a better terminology that will not distract us from the main point so by using a smooth regulator you regularize the theory and what that does is that essentially eliminates the infinite oscillator problem essentially makes it a finite number of oscillators problem and then you are allowed to add local counter terms in the Lagrangian all terms in the Hamiltonian which are local in the situation when the Hamiltonian has terms like lambda 5 to the 4 you are actually allowed to add terms which are proportional to this in that case you make some value of the lambda measured in experiment fixed and then you take the limit so the statement that I would make is that renormalization means that to this regularized answers of quantum field theory we are allowed to add local counter terms to the Hamiltonian so as to remove the divergences in the limit when the regulator is removed the low energy does not change the point is that actually this thing which we are setting to 0 it turns out that if you did the same calculation in 4 dimensions the measured value is actually not 0 so it can be this is to be provided by low energy physics next time I will try to think of a better way of saying this but the main point is that practically you saw that there was a divergence and I could simply drop the divergence by imagining that my Hamiltonian was different that is the main point that is important for this discussion and if I did that then I would obtain z of tau which is exactly the Dedekindeta function now you are absolutely right that a priori this q could have some arbitrary finite constant could have a left over and what is the principle which dictates this one principle is that the physical observables at low energy should not change in this particular problem there is actually a symmetry which tells you which is conformal symmetry at low energies you have conformal symmetry if you demand that then this implies that c is equal to 0 and let me make a short comment about the conformal symmetry because that is what brings us to conformal field theory so the basic principle is that you want to put a regulator and you want to define the theory by regulating it and you are allowed to do renormalization but you want to do renormalization following some principles namely the low energy physics should not change or the symmetries that you think should be there in the low energy physics should not be violated and in this particular case if you look at the equation of motion phi is equal to 0 this is invariant under conformal transformation arbitrary let us consider the real equation sorry in the Euclidean space del del z bar if I take z going to f of z and z bar going to arbitrary f of some other g of z bar then this equation remains invariant let me call this omega and this is equal to omega bar so quantum field theories which have whose equations of motion have conformal symmetry are invariant under conformal transformations they are called conformal field theories it is a conformal quantum field theory sometimes it is written as CFT and in particular in this case conformal symmetry means that if I just scale the only scale in the problem is the length so if I scale the size of the universe the energy should by just dimensional analysis energy should scale as 1 upon length okay so this other examples of conformal field theories example the theory that we wrote down df is equal to 0 d star is equal to 0 in 4 dimensions d is equal to 3 this is for the Maxwell electric U1 U1 it is also conformal invariant what exactly do we mean by conformal transformation you can actually make it more another way to state a conformal symmetry is that the equations of motion are invariant under if you had a curved manifold then they are invariant under while transformations so for example the Laplacian in 2 dimensions that we wrote down you know which is like d star d plus d star you can actually in some coordinate frame you can write it as del by del x mu square root of the determinant of the metric g mu nu del by del x nu let us just take a Euclidean or you have to put a minus sign here now if I do a while transformation then the determinant of g will go as d times 2d times the determinant of g g is the determinant this g is the determinant so square root of g goes as e to the 2 psi g mu nu upper the contra variant goes as e to the minus 2 psi g mu nu so we see that exactly only in 2 dimensions the scalar Laplacian is d psi and therefore this quantity does not depend on psi is invariant only when d is equal to 2 because then this term and this term will cancel what is the conformal field theory more generally if you have a curved manifold or if you have more general forms and so on what do you mean is that the equations of motion should be while invariant I am changing the metric psi is a function of x so it is local so it will not cancel so this will go to yes but there is a derivative here let me do it if I just do this transformation on this Laplacian what will I get I will get this times e to the d minus 2 psi x del by del x nu sorry g mu nu square root of g del by del x nu so this will be the same as before then you will pick up an extra term pick up this derivative term so this term will be 0 only when d is equal to 2 sorry here but the equation of motion will not change the point is that if d is equal to 2 there is minus 2 sorry what do you want this is correct right minus 2 yes sure yes I agree minus 2 but therefore the equation delta phi equal to 0 will be left invariant so this while invariance of the equations of motion in a curved manifold are closely related that is one way to think about the conformal field theories of course there is actually much more abstract definition in terms of purely of conformal field theory purely in terms of conformal group which we could have done but this is another way to introduce conformal field theory so I think I will stop here let me now just very quickly summarize what we did I think today's lecture was perhaps less transparent than last time but it's because we are trying to do more things what I said was that starting with quantum mechanics and harmonic oscillators the quantum field you could think of as just a collection of harmonic oscillators and you could do pretty much everything they satisfy the equations of motion and we I gave one very simple example of renormalization and what you want to take away from it is that by adding a local counter term you could deal with the divergence even though you are naively getting a divergent answer if you imagine that your Hamiltonian was slightly different it was possible to remove that divergence so there was a so the statement of renormalizability of quantum field theories that under certain conditions if the coupling constants are dimensionless they are called renormalizable field theories it is always possible to remove divergences I mean it's a kind of a physics folklore theorem physics theorem you can say really prove it rigorously is this clay million dollar prize for the QCD so renormalization theory is the study renormalization theory in general is the study of this limit epsilon 1 to 0 you have regulated with some regulator epsilon and you want to remove that regulator and you are allowed to add up to local counter terms adding local counter terms and the statement of renormalization is that under certain conditions you can always remove those divergences and all physical answers can be rendered finite so whatever divergence you encounter there are of course a lot more complicated divergences appear but this particular example I think is simple enough to you can really work it out there is a divergence and you can remove it and in this case the physical principle that determines that what constant why we don't keep some finite constant still hanging around is because then we ensure that the theory becomes conformal so your renormalization preserves a certain physical symmetry that you wanted to preserve ok I think I will stop here


Okay, let's get started. Good afternoon, everyone. Thank you for coming. I'm Sato Moria from Hitachi. Today, I'd like to talk about Ironic and the Cinder Integration. At first, I mean, I'd like to introduce myself. I'm Sato Moria, and I'm a researcher working for Hitachi, and my research topic is mainly improving open source software. Such as Linux, QEMU, OpenStack, et cetera. And yes, I'm OpenStack ATC from Juno, and my company, Hitachi is a huge conglomerate company, and so we have a wide variety of business group from IT, social infrastructure, plant engineering, and yeah, as you can imagine, we're a huge system. This is today's outline. First, I talk about background and introduce Ironic itself, and then explain standard storage support with Ironic. Let's move on to introduction. The background, our company focuses our business on enterprise system and IT systems, back in social infrastructure. In those systems, BMTL server are commonly used to satisfy their requirement. Those systems are really hard requirement for the reliability, availability, serviceability, and stability. And also it needs some performance, in particular, latency. But on the other hand, even in those kind of systems, demand for cloud is growing and growing and growing. So we'd like to use Ironic to deploy these systems in OpenStack environment. So what is Ironic? Maybe you guys know the Ironic. But I'll explain again. The Ironic is the OpenStack BMTL provisioning service. And it's like a BMTL hypervisor API. Via this API, users can manage BMTL nodes in the same way as virtual machine. This picture shows it. In the left side, there's a hypervisor and it manages virtual machine. And it also provides API, managing API to Nova. In the left side, there's Ironic. And Ironic manages BMTL nodes. And it provides management API to Nova. So users can control virtual machine and BMTL node via Nova API. This is a simple Ironic architecture. Ironic consists of six parts. Ironic API, message queue, Ironic conductor, database, drivers, and Nova Ironic driver. Ironic API is a service by which administrator and other services interact with BMTL node. And the conductor is a core component of this Ironic. And it does the bulk of work. And drivers. Ironic needs to support various hardware and deploy method. So Ironic introduces driver framework. This is an example. For power management, Ironic supports IPMI, MT, IRO, DRAC, and for deploy, Pixie, and Agen. And similar to other OpenStack projects, Ironic uses database to store bare metal information. And it also uses message queue to communicate inside Ironic project. And the last one is Ironic drive, Nova Ironic driver. It is not actually the Ironic itself, but it provides interface between Nova and Ironic. This is a BMTL node provisioning flow in the case of IPMI and Pixie. First, user request BMTL instance to Nova, and Nova does some work. And after that, Nova calls Ironic API to create a bare metal instance. After Ironic API gets the request, it sends that request to conductor. And then Ironic conductor gets image from glance and set up the network. And then after that, Ironic and the driver turn on the bare metal node and install OS image and reboot. The finally, user can use bare metal instance. As I explained, we can manage bare metal server, bare metal node, with Ironic. But unfortunately, we need some additional features to use Ironic in a business. One key feature is external storage support. Many users in enterprise area deploy database servers to bare metal node. And in that environment, external storage is commonly used for its data store. And the second key feature is network isolation. Current Ironic supports only flat network. It means all the bare metal nodes are on the same network. It's not acceptable for multi-tenant environment. These are another features I don't actually have. But these two features are really essential for us. And based on our customer's requirement, this presentation focuses on external storage support in Ironic. As you know, in OpenStack world, sender-managed external storage such as FiberChannel, iSCG, and RBD. So our goal supporting external storage in Ironic means making Ironic support sender volume. The supporting sender volume divided two cases. The one is boot from volume, and the other is boot from local hard disk with data volume. This picture shows the necessary function for each case. For boot from volume, Ironic needs to follow in functions, attaching volume to bare metal node, and install OS image to sender volume, and configure bare metal node to boot from volume. On the other hand, to boot from local hard disk with data volume, Ironic needs to attach volume to bare metal node, and install OS to local hard disk, and configure the bare metal node to boot from Pixi or local hard disk. Fortunately, sender and Ironic already support some functions. For example, the install or operating system to sender volume is always already supported by sender. And similar to that, install OS to local hard disk or boot set up the node to boot from Pixi or hard disk is already supported by Ironic. So to make Ironic support sender volume, we need following two functions, attaching volume and configure bare metal node to boot from volume. And attaching volume is common in both cases. So I set our goal is to support boot from sender volume in Ironic environment. This is a basic idea for boot from volume support. To boot an instance from volume, node, sender and Ironic need to work together. Especially, node should orchestrate them. Fortunately, OpenStack and Nova already has a framework for boot from volume, because it supports the boot from volume for VM. So why don't we use it for bare metal instance? So let's use it. This picture shows the boot from volume framework in Nova. First, user request Nova to create an instance which boot from volume. And then, Nova asks sender, hey, sender, please create a new volume from this image. And sender create an image and copies OS image from glance. After that, Nova asked hypervisor, where we connect the volume. And hypervisor answers the initiated information to connect to volume. After that, Nova asks sender to connect the volume to the initiator. And sender touches the volume to the initiator. After that, sender returns target information to Nova. It's number eight. And then, Nova passes target information to hypervisor. It's number nine. And after that, Nova boots an instance from it. The number ten depends on hypervisors. So in the case of KVM, Nova does mount the volume to the hypervisor. And they find the volume as a root disk and start the instance. This works well, only for VM. So what's the missing piece for bare metal node? Here it is. The missing piece are number five and number nine and number ten. And number five is getting initiated information from hypervisor. And number nine is put the target information to hypervisor. And number ten is configure hypervisor or bare metal node to boot from that volume. This is a detailed picture. As I explained in the previous slide, there are three missing steps. One is getting initiated information. And the second one is passing target information to Ironic. And the third one is setting up bare metal node to boot from volume. To fulfill these missing steps, Ironic should have following three functions. The first one is managing initiator and target information. And the second one is configure bare metal node. And the third one is communicate initiator and target information between Nova and Ironic. From next slide, I'll explain each topic deeply. The number one, this is managing initiator and target information. This is the main part of this enhancement, I think. To managing initiator and target information, we add a new table and attribute to Ironic database to store initiator and target information. And also add the restful API to create, read, update, delete, dot information. And of course, we enhance the conductor to go between API and the database. We already proposed spec for this function. So if you interested in detail, please look at this spec. Second one is configure bare metal node to boot from volume. In the Ironic, each deploy method is implemented in driver. For example, the pixie driver and the agent driver, the virtual media driver. So we add boot from volume driver. It configures bare metal node to boot from specified volume. And it needs to control the BIOS or firmware. And this driver, after the configuration, this driver turns on the node. Third function, this is a communicate initiator and target information between Nova and Ironic. Nova Ironic driver provides interface between Nova and Ironic. So to support communication, we add two functions into Nova Ironic driver. The one is get initiator information from Ironic API. And second one is put target information to Ironic API. The spec for this feature from HP, so if you need, if you want to know detail, please look at this. With these three features, we can boot the bare metal node from volume. So I'll explain the deployment flow. Before the deploy, we need to prepare the environment. That is administrator registers the bare metal node's initiator information to Ironic. So I don't maybe have initiator information at this point. And let's deploy. Use execute Nova boot and then Nova asks sender to create a new volume. And sender create a new volume and get image from glance and write it to the volume. And after that, Nova gets the initiator information from Ironic. The Ironic gets the initiator information from Ironic database and it returns to Nova via Ironic API. With this initiator information, Nova calls sender and asks, please attach the volume to this initiator. And after that, sender attaches the volume to that bare metal node and reply to Nova, this is the target information. And Nova passes this target information to Ironic and Ironic save it to database. And after that, Nova asks the Ironic to boot bare metal node from the volume. After Ironic gets the request, Ironic configure the bare metal node to boot from specified volume. And using target information and then Ironic turns on the bare metal node. Now users can use bare metal node which booted from sender volume. This is the current status. Now I'm proposing and discussing the spec for this feature. There are three specs for boot from volume support. The one is the managing initiator and target information in Ironic. And second one is Nova Ironic drive enhancement. This is from HPGuys. And the third one is a new driver to boot from volume. This is also from HPGuys and so it only works for each service. Also we posted patches which implement this specs bug. So if you are interested in this feature, please review and give feedback to spec and these patches. I'd like to these features implement in this release cycle. And to the next step, we are thinking of first boot support with sender back-end support in Glass. Currently the image copy to the sender volume is used by the network copy and DD. It sometimes puts a load on the network and IO. So with this feature, copy is we try to upload the image copy to storage. If you are interested in this feature, we have another session about this feature. So let's please attend it. To support boot from volume, we are trying to implement three functions. One is Enhanced Ironic to manage initiator and target information. And second one is a new driver for boot from volume support. And third one is Enhanced Nova Ironic driver to communicate initiator and target information between Nova and Ironic. And now we are discussing the spec and the patches in the community, so please review and give feedback. This is all I have today. Thank you very much. Is there any questions? This is a clarification question. You suppose you would use the hardware initiator, Ithcagi initiator in that case, right? In this talk, I only talk about the hardware initiator, but we can support the software initiator Ithcagi case. But we need some enhancement. Already? Yeah. Okay, I did some investigation. Thank you. And in the case of use of hardware initiator, you need some hardware support to configure the initiator from the network, right? So I suspect there would be a lot of compatibility problems between hardware vendors. Yes, so we develop the driver for each hardware, I think, each vendor. Okay, thank you. Hi, I have several questions from the sender. First of all, I would like to ask you to attend our meetup on Friday. We'll discuss something related to it. Sure. And what about security issues? Because if Ironic instance will access to storage network, what about multi-tenant networks? How do I handle it? So you ask me the multi-tenant network support? Yeah. I think there's another session in the next room from the Devananda or Jero or PTL. So I think you can ask them. Okay, did you try to make it working without NOVA? Because in sender we want to attach and boot Ironic instance without NOVA support. Did you try something like it? At this point I don't have the requirement that case. So I think you or other guides propose that kind of future. So I think we need to discuss by day. Thank you. Okay, any other questions? Have you thought about doing this without adding a database to the Ironic model by using instance info? Or what are the other fields that Ironic provides to hold information like this? I think we are discussing how to... Thank you very much.


Hello students. In this ELC video we're going to look at assessment 2. You will find out the main details about the assessment, some tips about organisation, some reminders about supporting evidence and referencing and some more reminders about submission.  OK, so first, what do you need to do in this assessment? OK, so assessment 2 is a problem solution essay. It continues from draft 1, assessment 1. Now in assessment 2 you have to write about 900 to 1000 words. You need to include a narrowed essay title, an introduction, body paragraphs covering the problem and proposed solutions, a conclusion and a reference list in the appropriate referencing style for your discipline. Right, next some tips about organisation. Please pay attention to topic sentences. The topic sentence should be the controlling idea of the paragraph. By reading a topic sentence, your teacher and any reader should have a very clear idea of what the paragraph is about. Try to include paragraph hooks as well. A paragraph hook links between your paragraphs and improves overall organisation. Also, try to end each paragraph with a concluding sentence that links back to the topic sentence. This will also help with your organisation. Next, supporting evidence and referencing. OK, so remember, you should have supporting evidence which uses reliable and academic articles. Your main sources should come from academic journal articles and books. You can also use newspaper articles, magazine articles and government websites. But you cannot only use newspaper articles. And your reference list is graded in this assessment, so make sure you get it right. Look at the ELC, referencing guides for more information. OK, finally, reminders about submission. Please do check Blackboard for the due date for the assessment or ask your teacher. You need to submit the assessment on Blackboard via Turnitin. A final tip. Submit early and look at the Turnitin similarity report, then change your essay as necessary. Use Turnitin as a tool to improve your essay. OK, that's it from me. Continue working on assessment 2 and remember, have fun at university.


Meme ni kama ni mechanga nikiwa. Litoa wapi denia itali wa watwang, what's the problem? It's okay. It's going to be alright. Alexus gave us a lesson. He broke it down for us, which I like because it's comprehensive for the ones who don't understand like me. I tried to perform on Facebook. I tried to perform a channel on Twitter. Hashtag is why. In the morning, it's a very energetic morning. Me na feel some type of way. I hope the energy na vibe na fikiya. By the way, slow clap to you. Wituza aka ebus kam... Mazi kam mulu na muntua wapi aki. We appreciate you. Starting with valentine number one, which just happens to be my name on social media. Color me that. Likini cha muimu apasini. Mkumbeni Y-5-4 Facebook, Y-5-4 channel on Twitter. Hashtag is why. In the morning. Or you can use our SMS line two zero one five four and start with Y-2-5-4. Okay. Tope kia leo. So na jwa kama kao. Jinafanya man crush Monday. Is investing in your bae. Investing in your bae. Is investing in your bae a good idea? Kwaishon Mark. But before we start that, let's welcome with open arms and their warm hearts our panelists of the day. Hi guys. Woo! Yay! I'm gonna say. Yon, yon, yon. Glad you guys are around. Thank you so much. What? Wana pre-taji is the streets. Ah, na ita wa braio. Ui. Siree braio na jo. Oh. Kewa kwa api. I'm dachana. Siree, akwa round. Akwa round. Okay. I'm not necessarily a kwa lord. I'm soft, soft TV. Already na kwa gopa. Ah, anu me kwa polia. Polia even though I find the most destruction. Not really. Kweli. Social media na jitaji. Na jitaji mc kare. Sasa umbonu metua braio kwa social media. You'll see what I'm talking about. Takini karibusana. Thank you. Hi, queen. New book of Vanda Stik. I like everything about you. Thank you. What is your kutne? My name is Sharon. Social media hands? Sharon Mongera. Yes. Everybody. Facebook. Not on Instagram, Facebook. Among Facebook. For real? Yes. Uta sumboa ita um. Hey. Amana skupu idea. Uchne zongia ideas badaik. I might even just be your manager. Aba aris pa. Sala maasa. How are you? I'm fine. Naka smati. Thank you. Onakutana nizu. Onanita John. John. Vivo tu kona jina mo daga mbozi. John o diya mo. Niku na suali wa tuwango. Since nimi ongelia mbozi nika fkirea mboa. Nimboa ya nani li kulambigiji. Wuz dog ehti begiji. And why is it a track? Nambore na suali wazu ribo. Musipotatli. I didn't bring it in, she was calling me. Wakena ni nili. Bala tu zidokwa denizatia hina, zidapan, ziditani tunakini. It's okay. Nawa penda tubure. So right. So what do you think? Do you think you should invest in your bank? Kamama nome. Roti li? Why now? Kwanza ni semi. Sipo akama venime. Sema kwa sababu. Yubi. Supe kia kumiyo na yubi. Mimbi anizakwa na someone else. Bench to invest in. Nani li skia abischa ni wa kutuki wanae. Ya. Aki tokatu from the eyesight. Akuna niya jami. Kabisa. Ona venim na kubali. Is it true? Do you feel the same way? No. But you do. Konakunga na ii suali. Who? Why and how? You are investing in who? Na jo kuna beveni me kutana tu for a short na na hendanga kiyen. That's for a shorter duration. Kuna mutu, mimi me kunae for a longer duration. Mimi kunae through thick and thin. And then why am I investing? Na invest. Bona na invest. Maybe sometimes me kunao mutu through thick and thin. And then you feel like I want to support this person. And how? Sila zma ni wuze. Shamba. Mimi sezi wuza. Shamba. Na invest kwa be. Ii yo kama ni. Yo na chana na hendanga. Ata kama tu me kunae through thick and thin. So these are three questions. Uki zi jibu vizuri, ubalans. Ya. Na eza invest. So just in that line of thought mami, I'll count in a second. To say me that who, ni mutu unona kuna potential. That for the basis of our topic. The who here, zin ube. Ni na nisi ati mwenye tu. Ni me una video ingine braio na kevo vinyana jagulwa stanu. Nona. Wana piti shama avocado hibi. Hibi tu. No, not like that.  And that is just for the purpose of the show. But kama ni kuna pesa? Kama zina asasana nita invest na nini? I like that you said that. Who will come to you shortly? Aya. First of all, hibi tu ndekwa sosomidi aya. Deo izi chomensi. We have oteno na shiaz oteno. There are particular points when it can be healthy that is investing in ube. This is when you are sure she will marry you and whatever she is investing in will be beneficial to your family. And our social media guru, the one that he has some, Keeta has asked an important question. How do you know she's won? We have Ken Key, Gangster. Man, it is hard to get one for ladies. So all you do is play them hard. Maybe one day you'll end up winning the game. Wait, in this case getting a better half. Ain't nothing to worry about. I see Silver King says money brings girls and girls bring lies. Wait, wait, wait, wait. So spending on a lady is something that won't benefit me. Any way is something I cannot do. 100. Okay. On any of your means, when you are a man very close to my heart, you cannot be broke and expect not to be cheated on. Relax and enjoy the title on me. So title sapo ni betu. Uhuru Kevin Owor says Sai boichald ngungori jo. Waka wambia talk if you have kwa something in your poke. Doma unona magalde most when I end up kwa frustrated na kubakia single parents kus boichald aksha chanuka kwa pala after his money anaka temamba haia. Na po ume waste time mob. Chene magaldem hawa jatambua ni once ume vumi liyam se kamaik pamoja hukupanga hukupanga respect fenoma. Oh, kweili. Sosa veni umesa matruthi kwenvena. So ya blacky shade, he had something to say.  Some guys are just being used by ladies to come pain in the breakups, parental issues, life issues, too much work or money. Too much money.  Guys are used to show off. Guys are used by ladies who are pressured by their peers. So it's healthy to not where you are in a relationship with a girl. I'm talking through experience, watching from 125. I see you Sophie Ru. I can't depend on someone who also depends on his parents. Pull it up. Pull it up. I can't depend on someone who also depends on his parents. Love is all that I need, not money. Young Jay Brad says, no, it's not healthy because you'll be the only one in the relationship. Kweili. Ajay. Hmm? Nani kama tumesoma izironim, K.E. and Huru Kevino where I see you. I see you. I see you. Remember to use the hashtag what in the morning. White fire for Facebook. Ibrahim Bailon says it had depended pesi ati umanam jengandho. Kila time ati eachuna en hue ako jenu anatoboke. Patrick Pogbas says mimigal shahudi kani cha periastoriadou na periarredkat. Kamahaukoma do wa like naba kisingo. Atumama demo natu kakwanzi kwa nziyat. Aakuna de, manachika kwenziyat, down grupa mocha. Kweli. Ken kai... Nonakweena ki defa nawai ama ichunenda twa pusa, we have Ken ki against the man, it's hard to get that one lady, so all you do is play them hard now not count in the summer, you're ready. And ain't nothing to worry about. Manzi, please give me your thoughts and what you want to communicate on the topic. The topic is investing in the day. Is it right? Is it healthy if you have Joseph Boyo says no, no, no. That is welcoming poverty. Of course, I invest in Bay, but I must have a vision. I invest in Burebure. Now, I just ask you for a friend. I can't tell me if it doesn't have a car. No, no, not. Okay, when it comes to investing in Bay, kuna viduta consider, of course. Apatunongilewa, when do you invest in Bay? You are the investing. And the investing, of course you should invest in me. Say, look good. I should look good. Eh, eh, eh. And do you agree? Say, you should look good. I should invest in Bay, but if it doesn't have a car, it's not going to be a service. It's not going to be a service. Ah, yes. That is one thing that I know. I don't think if true love exists now. Clearly. What kind of love do you think exists? The love I think exists. That is what Brian is talking about. Na seti wana yosai dingine, but continue first. Eh, sayi ni bapensia pesa. Uhu. Kwa nizos kusini na kwa na pesa? Kudu kwa nazo. Lakin ni, kuna kitumoja, kuna mutualisa mevi. Kupenda, kazi ni kupata kupendae. Manake, waleboengi, wapenda, kileu lichonat. Nandiposa, I don't think if there is true love exists now. That's why I cannot invest on a be. Not unless now we marry, then we continue investing together.  But before that happened, tell me the truth. Why is it that ladies are not allowed to have a preference aseme na tkachalia kuna do? Nani ni muneza chagwa, karoha na haga aki. Wacha ni hende na ni, wacha ni hende ati, nama sudi ni nani, mania na, me umbo ya kutosha. Kaisone sa kujapa kwa mbe teki ya kere inaka. And he will not deviate. Akun na mtuonata, mambe ya hende evi, berla kuende evi. Namshaji seti. So situ jiyue.  Mbo na siya twizi chagwa? Still you have a choice. You messed up a bribe. Still you have a choice. Karibusha rungu. Nasa maivi, still you have a choice too. And... Mbo na kwa milia pwutagi kutua pesa. So uto aitu? I can. Ati kwa api. Ido manu na sinikuji tuu, mam. Mi tagi kubumpa teki. Ido tu bha bi kota situ matatu. Isawa. I can. But we learn from experience. I have tried that. And that's why I said ma, it's time for me to believe that there is true love existing. Because I tried my best to invest on it. But unfortunately, after tu me patiki dogo, ya kwa kisungu. Mi ni kwa bi kabadu. Kapa na iwa. Green pastors. Green pastors noko. Mi ni kabaki tu, iwa tu. And I am already trying to invest. You see? Mi kabaki surrender. So to say ma, you're better which you make up? Kabisa. Help me understand. Onajiwa, kuna one thing mimiak like, ono na watu niwa kukwa village setup. Let us try and think like watu niwa kukwa village setup. Pale paletu kunyumba, nitura daza ko, usikutu na ndakutua, biya takaki shapu lakuwao. Ya na kuja tu kuwenyuku lala. Subwitena na raukana ndakuao. Ono na. Those days are really enjoying. Ono na. Sii maisha itu, ni mada o, ni mili ni, ni mili ni. Iki tu ina tuwa. So I think na watu ni are really enjoying life. Iki tuwa, ni mada o, unataka muna kuna pesa. Bona wei una iwa pesa. Siu ngekwa na iwa unge takaka muna kuna pesa. Sasa mimu unataka nitu wei wa api. But you're the head o. No, who's the head? Uta uta ni kali ya useme, bufa. It's hard time not to try.  Ato kuja useme, ben atkaku end out, when did? Why now? Why now? Nene mese maio. No, wei uki taka muna kuna gari wei, nene yo gari unataka. Aha. Yaha. So kumukuna gari utaki mutu menyakuna gari ni sawa, butu una gari, una eni. Talk to him. So unataka kuni yambia should not look higher. Not looking higher, looking higher. Aparenti wuna faku baki tuwa. Ni baki tuwa. Yani juie hana pesa. Uwana liya tuwa na umehawa? Hawa na. Nga wei niwa kuna utuna fanyani. Wei niwa kuna usi wana eni na notu wei niwa kuna ho. Okay. I think that is how life is played. Sasa si, chesna na ligiya ako. Chesna na ligiya kuna ni. Wei niwa kuna usi unataka kuni daka ligiya wei niwa. Uta kuwa frustrated. Wei niwa nunga John mkono. Doko. Ngei niwa po Arakazaka, Wepecon Facebook. Let's start with the slides. Is investing you in your significant other a good idea? Is investing in your significant other a good idea? Do you think it's a good idea, Queen? Yeah, it is. Why? It's your significant other. But um, javisha na pete bado. We said this is for people who are in a serious relationship or are hoping to be in a serious relationship or may not have potential. What was the situation she was in? It's just for serious people only. So for serious people only. So there is there is reason. Of course. Why are you serious with each other? You trust each other one. So why not invest in you? I like, why not? Why? Serious. What's a serious relationship? What is a serious relationship? At first. Latina ni mauliza berayo. Nasa kwa kudua. Tapuni ebe. What is a serious relationship? Serious. Eving, kwangu, nisa seman sila, sinire sasa. Nonome fikiya kihwangu ya kuwa na kulewa. Sio kama asai. Na juwa kama asai unesakwa. Berayo, naim. Onha juwa, in this relationship ni matwa willi. You can feel kwa sa idea kwa this is a serious relationship. Kwa ilisai, doi namba 5a? Manaki ni disemi. Kupenda siya kazi. Kazi ni kupata kupenda e. Nono. Nesa kwa unapenda e 100% nizu kwa unapenda ui udim nopenda e kwa yote. Non, fiyaka basi. Lakin ni kwa ke yohata ui koto penda. Ui kutu penda. Ui kutu penda. Nono. But okkama ujuiziti kama asutana suwambiwa. Ukiwa, anu kiolewa unata ofta manome manyana kupenda kupenda za idea fiyaka unapenda. Am I wrong? Am I wrong? And why do you think that is?  Looks what? Looks sitna zeka siya wote? Sisi wote tuta zeka? Yeah. Yeah. So usit after ok mi na mianga most of my friends usit after looks look for character that never dies. Never dies. Looks. Arame ni kiza kufkos. Taka iwi niko. So wacha ni kulize yohata unata kua leka. But sisi bada una cheza tu kamawewe na wa kina? See that is the problem right there. Right there. Una cheza kamawewe Una cheza na nani Una cheza na nani Una cheza na rohue na nani and why. Ono ui ame chezwa. Yeah? Ui manzaka mi niza bao na look at how he is defeated. Ate he cannot imagine and slow love exist. Bono na na cheza na? Why? No. Jibo why don't? No we are. We have question. Sisi ni yohata na cheza? Sisi ni yohata na cheza? Sisi ni yohata na cheza? No. The first thing kuna one thing value you need to understand was yana ni wengi and we need to serve was yana all of them equally. Sisa ina bidi mi kisha maliza na nani nani bia na ni itaji. Sisi we need to import one woman from China. Sisi tu. Sisi kamawekina. Yeah? Inajiwa lasi matu cheza kama Sisi kwa ile kori doa na kuitaji yuko alafu mchazem alafu mchazem sasa skia. Yes. mchazem kwa bihbaya wasuki kwa bihbaya. Banzama numi anapata kaha to break moja moja when he was 12 years old. After that hakuna and then oh my god my heart is broken into pieces. This is where hakuna time hakutafta super nuku stitch kidaba. Hakuna ni But inajiwa ina naliga na level of heart break kuna ina na pia level of heart break. Aha. Yeah. You just say heart break kwa ebu mongi lesho? Eh. Wewe inajiwa kuna heart break ingine. Ganiyo. Inajiwa kitu mekutana na e tru apu kido e ya compass Inajiwa compass love ni like iini kiditu mekutana na e kwa compass ni mam ola enough I know what I want from the university. I know what you want from the university. First year pala kwa line to nine registration o kaniwa nyeshia si dwi lu o kainki ya box What do you expect? Without children nisekiya pressures on enkiya from today I hope you're hearing how this may not work. Nami stay and we can hear loud and no but but I hope us here wu ya ki kumbe rena ni mi rempu you're the most beautiful girl who can pass jo mengi ya juu zi uji rena na kwa Are you hearing the way they are talking about baby, baby stay woke How far is too far when investing How far do you think we need to bali manome aku baie vitu ama si me see vitu he pays your bills o kido kudogata achangie skufi we watu tamu we help me Ina letanga shida badai Why? I'll not lie because it afica point the guy only like anisekiya anapatiya pressure oh you're not supposed to go out with our guys you're not supposed kwanza wile umewa ni pesa angu you're not supposed to dress like that no kuna I think of our situation that trended a bit ago this lady have and this is just for information sake we're not going to assume that we know everything that happened in this particular story and we're not advocating for you to pick and borrow from what happened to this particular people in the story so the lady was studying medicine like you know shalikwa anasume maali alafu tukifuatili astoji but according to mainstream media ilikuna semekana udemali kuna mitishado anatuma in thousands in tens of thousands anatakahi anatuma anatakahi anatuma atu jik kachali alikuna faini me personal business jatakazi alikua ni anatuma anatuma does that give you a right as a man sasa kuni yambia sasa ni kama ni mekubai sasa ni kawneka depositi mahari is that really what you telling me and how would you feel as a lady wunai tisha pesa ama wunai tisha vitu yani tukuju spoil ama jua mesama ni wako and he do anything for you but suddenly since amefanya now he has shares in your life do you think that's fair to some extent it's not fair because okay boi chal tuna jua ni akupati okilakitu wuna vitu ame piti anahakombi most guys don't actually tell you they will not tell you ata wupusha juo hard aata kambia ni kona kainvestment apa kana kani pati atu ka pesa ka pesa saizu amelda kufuliza amelda tala amelda branch just for you just for you so it's okay it's not fair because anyway atawe you can work for it part of it you can work for it siya ti asupati e pesa if he wants to give you money let him give you Lord you ask him e pati e pesa siya tali pa rent ni pati e pesa siya jofanya ni pati e pesa but now na ni kama kuna nana penda kuitisha in fact usipoma itita ata uleza unetisha wapi nana kumalina ni true story I have a friend who if anona tu via tuivi atasem atam tu mi skrinjota semi na taka ya atasema dan am tu mi hella that's how it works that's how you want to be treated am na ataka aji no kali bisha rungutena mi na sema afadali mi mone ni feel I want to give you something instead of you requesting me not unless wukona imagine so that you cannot avoid kwanza puko imagine so in the woman na endangata offline kuna imagine so in the woman emergency offline kuna ilia kuzo na jokunenki na mezwe kuna imagine so in the woman 3rd time nijoha wuki zuia sana atam mi na tako zuia tu wuki tu ma imagine so na mi na nasi mnusidia on weh weh weh kuna ime atulisoma tekstiyan wuk gani ili ulu kuna ni om batri ke Ya, yo, bados jasoma. Bados jasoma, yo. Muna tupe ma. Dr. Kuliza Spali. When should one start investing? When should one start investing? Two, three weeks after dating? Longa? Immediately after you start dating? Again, when should one start investing in their bed? Two, three weeks after dating? And this is serious dating, please. Longa? Immediately you start dating? When is the right time to start investing, John? Um. Um.  Hibutu? Soho Iniliye ingama kapu ... Ya ... Eniliye inga ... We are not playing the game here anymore. This book me at 12.54, at 12.54 turn on to the hashtag, is why in the morning. Is it alright for her to demand for things? I think to Misha Guzeva, let me just read it out loud. Ijia kudeseme, I can't get a girl with a car. So you buy a car. I can't get a broke guy. So you shower her with lavish things that you might not be able to afford. Na kwenu kumeni jibubu suresana? Did you please repeat? I like that you said Silas emotional mistimi. Yes. I say, Silas nani kumbe nipati e. Like if we are really dating, you should want to give me. Not, kila siku niko hako nipati e nipati e no. Ude kumhenti e, nini nisha wanyo ele? Kuna niso atu kupati e na hint, but it should come from him. Shikahi niku pati e, enda salon zaza. Laki nini hindi omta complain valentine samzebe wa kitu su na kataeze. Una kwa mhambosa e, bach timesa, Christmas cv, valentine valentine nivi, you want things. Of course, if you are valentine, see... Yoni ovia? Yoni ovia, na Christmas yoni ovia. Iri kwa ovia skuako? Yes or no? Apana jeskimi e yes or no? Yes or no? Eh, Ryan yes or no? Na umeva red, so choose your words carefully. Ata valentine, nisi juli kwa lini? Anatu pima. Anatu pima. Birthday valentine. Ya, ya, ya. So very smart man. Apewetatu, stu na pewetatu zanini, but apewetatu. Next slide, guys. We are on a roll. Watch for Facebook, Instagram, and Twitter. And the topic is investing in your pay. I work in the last soku nifunyevo. Chuta fika place tani pati e lika short summary and maybe a sentence or two of what you think of the general topic. So if you're advising the guy, the boy child, or you're advising the girl child, wukwe akwadi ngisawa. Next question, should she want to go back to school and you pay her school fees? Ya ni literally investing in her future. What do you expect in return as a man? I think this story, you may send so many guys to jail. Kwele?  Ni kwa umumbe, ni kwa umumbe. Ya ni kama you are their property. Ya, but sasa, paying the school fee for me is doesn't mean ni kwa pay your school fee utaba kina mimi pamanendili. Sometimes if you feel like working away na nili kwa na pesa, I'm still stable. Even thank you is enough. Mimi boratumeni. I thank you, I enjoy your time. You pay my school fee and I'm financially stable. I'll let you go. Is it all in the truth? Is that how a man will respond? Ya, for this case, nisa sema emailin so many men's mimi in trouble. So I know of a real story of two guys wa li fanya kulipa fee of a lady. Afterns, whether moja kwa ni ni US ni Dr. Yuka. Na bibi waken, u ya li kwa na li bialent, wa li kwa kama, they are coupling but kwa kumio. Na li kwa nga hukuni ni macha kosa. So, your demon kwa na sumia, keiyo. Afterns, after kumali sema sumia, kikulipa everything, na o deredi aka pata mano mimi gini, aka chumokaibu. Na na, the guy wakata dirudu kukenya, aka pata, deredi got married, belolotimu. After paying all the school fee, everything, he kitanda everything for that, didn't he? Everything, total everything. He's a doctor there. You see now? And last recraving that he went mad again. Atai shivu. That was the party that atai shivu. Kwa saka onasa, ne daku kukudestroe. Mimi nao was the next day. Deredi saka waso another man eno, alifanya the same case, aka li piya awa li kwa most, even paying kino about the relationship. He paid school fee for that college girl. After once, atau yo, da the college girl kumali zanga, ah, she got inini, aka chagulu wakua polisi. Na after once, after kwa polisi, after kumali zayote, kuturukua poliskamp, alitokana, bwana kuna chagi. So they man left frustrated. But you see? But Val, mimi from that statement, napenda kwa mbi awatu, this simple thing. Temi yuna pelika, this person maybe initially she was a high school girl, muna pelika to university or college. Like me, I like giving example with myself, because initially I was in the village, I used to date village girl. Uka kuja town. Where were you when you were in your life? Just get me. Sorry. Yeah, I didn't because you mentioned it. I upgraded to town, I got a part-time job. So, temi nyewepia umutu, just to be kwa yu mentality, yu umutu maybe, atakutana na awatu, because maisha kepia, watu enyana interact with. Inevolve. Yeah. So usi kwa na fixed mind, ati umutu akiludi nimi mitu. No, sometimes you let these things go. Ah, yeah. The last two slides, if you'd allow me please read them, to read to them. Is it possible for Bay to be too demanding awani manome hana kakitu? Tusha agri, manome na konapes, aiziaans of complaints utu mingi mingi apa. Is it true or false? It is true. Manome hana kakitu, nuyata ito piksandre me gru. I am next and last. The last slide, guys. Remember, thank you for watching. It's 1-24 Facebook, at 1-24 channel Twitter. Hashtag is 1 in the morning. The last last slide, sorry. So, nustana, they claim to be empowered, but still expect to be catered for at these double standards. Yes, yes or no? One word answer, guys. Yes? No. Omitana ni. Yes, no? No. No, yes or no? No. Last slide. All right. Last absolute slide. Cha ukuelot, cha ukuelot, kenaga, guys. In a nutshell, what are we telling the ladies? Wakai kwa mama yao. Kamana tchotia, kain na mama ke uko. As a sumbuwa. Kwa mama kia sanai we? Hi. You advise the teams according to the ladies. Kwae na sasa. Queens, listen here closer. Wakauku. Ni kwa pi, ah, yes. If you're dating, try not to expect everything. Of course, not everyone has everything. Some have something. So, the little he has set around there. Don't expect everything. Also, work for yourself. You have two hands. Like they do have. Two legs. Like they do have. If you're disabled. People who are disabled even work better sometimes. Kwae uongizia we volume. Yeah. Yes. Hi. Ni kama Mrs. Nengia, but I cannot seem to reach them for one reason or another. But my parting short is, please.  For this week, I just want to see the machine na nani. No. Yo dogi na nani. Dogi na nani alimpatia yo bingiji. Thanks. Yeah. Mkuna skupua. Please tune in tomorrow for entrepreneurial Tuesday. It's money making days. So, you don't want to miss it. I'll tweet for Facebook at Y254. Channel to the hashtag. It's fine in the morning. Or you can get us on our text saying 20154. Start with Y254. Have an amazing day. This is all the way. Bye bye.