Skupaj. Da. Skupaj. OK. Myslijo da podemos začati vsevno. Vstupaj smo začeli srečke lektu, na nekaj tukaj sebev, z njeljavnimi in različenimi vsevnoj 2-1-zimesnimi quantofil teori. Počin. Češo. Zateljno da smo na ICTP, začo je prvi visit. Vsah je prijevno, Zelo bom bila tako čutim v tem, da sem si zelo srednje. V moj boženiji manje drzili prej od diy v tju začutim na velime, in božem otvari. Puputim me iz temptedi, da po zdaj si neko razipravim, ne boš, da boš, da počutim, kaj si nekaj. Count det kako mora srečenik na kondensemözim fiziko. Srečenik na hrečenih energijov, všim njo. Z � CAM. Aha, nekaj je vrečenik na matematik. in in vsezivno, tako je hodnje energijne fizika? Daj, da se mi... In kaj so mnogo, nekaj je studenci? Vsezivno, nekaj je studenci. Zelo je zelo. Zelo, da je zaživaj, tudi je zelo, da sem vsezivaj, zelo, da sem vsezivaj, zelo, da sem vsezivaj, in zelo, da sem vsezivaj, ne zelo. If you want to read the references everything I'll be talking about was basically to my notes is copied and pasted from papers I wrote during the last 2 years and they have complete list of references. I start giving the references especially given that the presentation will not be in historical order, it will be very difficult. Because things that will look completely trivial from the point of view I'll present Pro blocks and them here, were completely non-travel when they were first discovered and it really made it very difficult. Second general comment is that the level of my presentation and the needed backgrounds would be total, totally uneven. There would be some things that look completely elementary like the first half of today's lecture, there would be some concepts there that I will use later s mešljenji, da sem bilo, da bo to zapotrati. InIf you think, this is to trivial, I know that, please, please, please don't decouple from the presentation, because various comments I'd be making in the trivial things would be connected to things later. The flip side of that is that some things will be quite sophisticated, maybe towards the end of this lecture načom vse. In ta, če energijame played, vse ni razdužili ga v tom, da so lahko sajno. If you find something too complicated or too fancy, don't think oh yeah, I lost, that's the end, I'm not going to pay attention any more because most of what will be afterwards, this will not be essential, although knowing the deeper stuff will really help. So, I am going to start with a very simple quantum mechanical system that I really love because you can learn an enormous amount of physics from it. And this is the problem of a particle in a circle. So, we have one quantum mechanical degree of freedom q, which is identified with q plus 2 pi. And we write a kinetic term, so there is a Lagrangian, ki je 1,5 q dot square. Zato sem si však odložite sistem. Zelo je zelo, da je vse simetri. Zelo je spektrum energijov. Zelo je momentum pi, ki je q dot. Zelo je energija, ki je 1,5 p square. Zelo je vse funkcije. Zelo je vse funkcije.  Zelo je energija, ki je 1,5 p square. Zelo sem vse zelo se zelo zelo. Zelo je vse komplikatno, da je zelo zelo elementri. Zelo je zelo, da je zelo v rovi, delta over 2 pi, q dot. Zelo je vse nekaj, da se vse nekaj, ki se zelo izvečilo? Vse svoje Mercuryo ne ga se vedimo. Zelo je vse, da je zelo, da je oklopo vse. Zelo je ovo, da je vse k glasbene, ki je x pi, ki je, da je zelo 2 pi. Zelo je vse, da je vse, kaj je zelo, da je zelo analiziračne z tem, da je tudi pravno, da ne se tako ne zelo. Zelo to je izgledo, da je vse. Tako je momentum. Tudi da se pričelim pa. To je ampak, da je vse vse. To je zelo energija. In energija je nekaj zelo, da je pi plus theta, nekaj ne boš vzela, ali da sem tukaj vzela, da je minus i dq minus 1 over 2 pi theta square on psi n equals en psi. The wave functions will remain the same, but the energy will be that theta over 2 pi 180 square. So what does the spectrum look like as a function of theta? So this is the energy. For theta equals 0, there are states, there is a state here. There are two states here. There are two states here, et cetera. And the states have energy as a function of theta, which live on parabolas. So if theta not equal to 0, the degeneracy here is lifted, and the degeneracy here is lifted.  And the physics is periodic in theta, but the square is here. Thank you. Thank you, at least one person pays attention. And so these are the energies. And the degeneracy that was here, you could ask, why was there a degeneracy here of the states? The degeneracy here in the states was that when theta equals 0, there is a symmetry that maps q to minus q. And for all theta, there is a u1 symmetry that maps q to q plus alpha. So these two states, this is the state with n equals 0. So this thing maps the state n to the state minus n. So for n equals 0, there is only one state, but the states with n equals plus or minus 1 are degenerate, and the states with n equals plus or minus 2 are degenerate, et cetera. So these two symmetries, which we call these p, or charge conjugation, or parity, these two symmetries together give us an O2 symmetry. So the global symmetry of the system at theta equals 0 is O2, and it turns 0 theta. P is broken, but the u1 remains a good symmetry. Furthermore, the Hamiltonian at theta is conjugate to the Hamiltonian at theta plus 2 pi. And I leave it as an exercise for you to find the transformation that conjugates h of theta to h of theta plus 2 pi. It's completely straightforward. Give you a clue, it's like e to the iq. So if you conjugate the Hamiltonian by this operator, you find the same thing. And therefore, you'll learn that physics is periodic in theta, because the Hamiltonian is the same. We just conjugate the Hilbert space. We can also see it from here. Imagine time is Euclidean, and it's compactified. Then the integral of q dot is always a multiple of 2 pi, because the integral of q dot is the multiple of the periodicity of q. And that multiplies theta, and therefore physics is periodic in theta. Another way of saying it, this system has instantons, which in Euclidean time go around the circle in Euclidean time, n times. And configurations as we go around the circle n times have a weight e to the i n theta. But since n is always an integer, physics is periodic in theta goes to theta plus 2 pi. But that means that the theta equals pi. So we learned two facts. The physics of theta is similar to the physics of theta plus 2 pi. All we need to do if we look at theta, or we look here at 2 pi, the spectrum is the same. See, there's one state here, there's one state here. There's a degeneracy here, there's a degeneracy here. And it keeps going like that. And the theta equals pi, physics is different. The theta equals pi, physics is different. The states are degenerate. There's a degeneracy here, and a degeneracy here, et cetera. And this degeneracy also reflects a symmetry. So the fact that the theta equals 0 is the same as theta equals 2 pi, that follows from this periodicity. And the theta equals pi, there is also a symmetry p, call it p hat, as we use the same notation here. So there's also a symmetry p, which reflects, so p generates q goes to minus q. But if the theta equals 0, it maps n to minus n, and that's why it's responsible for the degeneracy The theta equals pi p maps q to minus q, but it maps n to minus n plus 1, which is consistent with the degeneracy here. This state has n equals 0, and it's mapped with a state, which is plus 1, similarly for all the other states. So the map of p, the map of p of the state, p is a symmetry. We say the theta equals pi is invariant under this transformation. You can call it time reversal or charge conjugation. So that's what the symmetry is. But what is surprising, so that's the standard statement that theta equals pi, there's a new symmetry. But I claim that there's something funny here. The element p here combines with u1 into o2. But it does not quite combine with u1. For o2, theta equals pi. The group is a little bit different. So let's analyze the group. So we still have the u1 generator by alpha. So we gave it a name here, o alpha. And that's the operator that performs p. So o alpha takes q to q plus alpha. And therefore, it maps n e to the i alpha n. This is a transformation on the states. So let's compute p with q alpha.  So if we didn't have the factor here, we would have said that's perfectly reasonable. This looks like o2. We do a rotation by alpha, we reverse orientation, and then we do a rotation by, and so we reverse orientation, we act with o alpha, and we reverse orientation. Again, this is the same as rotation by minus alpha. That's the standard o2 relation. So the parity and rotations do not commute. But here there is another pre-factor between them. So at theta equals 0, we got the standard o2 relations. But at theta equals pi, we don't. Notice that this is not some fancy map. This is almost the simplest quantum mechanical system you can study. There is a complete solution on the block board. All the wave functions, all the correlation function can be computed. There is really nothing sophisticated here. And yet, we see here something very subtle. The system at theta equals pi appears to be charge conjugation invariant, appears to be u1 invariant. And when we try to combine these transformations, they don't quite combine to o2. They combine into a central extension of o2. Let's call the central extension. In fact, this is something that was known already to Wigner. Wigner said that if a classical system has a symmetry group, in this case, it's o2. So he couldn't quite study this system, because theta does not appear in the classical physics. But given that, the system has an o2 symmetry. The operators are in representations of o2. But the Hilbert space might not be in representations of the symmetry group, so said Wigner. It might not be in the representation of the symmetry group. It might be in a representation of a central extension of the symmetry group. This is quantum mechanics 101. And we see it here. So there are a lot of things we can say about that. The first thing we could say is, let define the operators differently. So let us define v alpha to be this central element e to d, but with minus 1 half. So e to the minus i alpha over 2 times o alpha. If we do that, then I leave it as an exercise for you to check that we do have the correct relations. That's good. We basically pull this e to the i alpha and split it evenly between the two sides. The problem is that now v of 2 pi is equal to minus v of 0. So we have doubled the number of v's. Another way of saying it is that the symmetry that we have here is still isomorphic to o2, but it's a different o2. In other words, as we make in o2, when we make a 2 pi rotation, we come back to where we started. Now if we make a 2 pi rotation, we come back to minus that thing. So we have to go 4 pi around to come back to where we started. So this is a double cover of the o2. We can call that pin 2. That's standard notation, but that's not important for us. I'd like to get another perspective on the phenomenon we have seen here. So this business of the quantum mechanics of a particle on a circle with theta was fully understood in the 70s. Believe it or not, I was a graduate student like you and I learned it there. The only new twist that I'm going to add here today is that I'm going to present this whole story as an anomaly and going to interpret it in an interesting way that will be useful later. In order to do that, we're going to use a trick that is extremely powerful. Whenever we have a global symmetry in the system, we would like to couple the system to a classical background field. This is not a background, this is not a gauge field that we will integrate over in the functional integral. This is just a classical background field. For example, you have a system that has your one symmetry system of electrons. You can put it in a background electric field or in a background magnetic field. If it spins, you can couple to it and so forth. So we can couple it to a background gauge field. So our Lagrangian will be almost what it was before. It was a half q dot, but now we'll put an a0 and it would be a square and then there was a theta over 2 pi and there was a q dot. We'll put an a0 here. And so now the Lagrangian is invariant and the gauge transformations provided a0 transforms also. But a0 is a classical field. We are not integrating it. It's not integrated over in the functional integral. This a0 is used as a probe. We put the system in some non-zero background field. We don't sum over the background field and now this particle moves in a non-trivial background. The system is still solvable as we will soon see. When we turn that thing on, there's another term we can add, which we can call it, well, there are various ways of calling it. This is the term that would be most similar to the Chern-Simons term in higher dimensions. And one way to think about it is that everything here is gauge invariant. So before we had a transformation by alpha, we can now, since it's quantum mechanics, we can put a gauge transformation alpha of t and provided a0, the background transforms also. So these two terms are manifestly invariant.  And if we would like the total derivative to integrate to zero, then k must be an integer. So this is very much like what is common with Chern-Simons terms. Except that this is a quantum mechanical version, so it's so easy that people try to dismiss it, but a lot of the physics can be learned already here. We will refer to this term. So a person who was not interested in this a would not even have the parameter k. The parameter k enters the scene only when we turn on some a. And that's an ambiguity in how we couple the system to the background field. So we can couple the system. So I wrote the Lagrangian before and I asked how do I couple it to background field. So there's a canonical way of doing it, which is what these two terms do. And then there's freedom with an integer. And you and I might take the same Lagrangian, couple it to a0. This is the only gauge field in the problem. And you and I might pick a different value for k. That's right, that's perfectly right. What that would mean is that whenever we consider the response of the system to background fields, you and I are going to get different answers. But that's okay, they are labeled. This ambiguity is labeled by an integer. Now let's run the same story again with nonzero a. So now we'll see what happens here and why we got all these phenomena. The first thing I would like to say that the only gauge invariant information, a, okay, let me first do it with nonzero a. So the first thing I noticed when we were already here, we'll go through the same story. So what are the symmetries? There is a global symmetry, it became gauged. There was this symmetry we called p, or charge conjugation, and that flips the sign of q, so it should better flip the sign of a. So a0 goes to minus a0, this is this charge conjugation. The symmetry looks like o2, so far so good. Let's see whether this is right or not. If we shift theta by 2 pi, the Lagrangian is shifted by, to 2 pi cancels the 2 pi by this. This term integrates to an integer, so let's take it to Euclidean space, it integrates to an integer, and therefore it doesn't matter. But this one does not. So if we shift theta by 2 pi, this Lagrangian does not go back to itself. Even the action does not go back to itself. So under theta goes to theta plus 2 pi, the action, which is the integral of l with values of theta, and k goes to the action, which is the integral of l, but now 2 pi with k, which is the same as the action with theta, doubt the shift by 2 pi, but with k minus 1. Okay, sorry, plus 1. So when I said before that the system at theta, in the theta plus 2 pi is the same system, that was true when I did not turn on this background A. But when I turn on the background A, that's no longer true. The system with theta and the system with theta plus 2 pi are not exactly the same system. When I turn on A, they have different values of k. In fact, I said before that you and I might couple this system to a background field in a different way. We turned on this A, so the first two terms are canonical, but the last term, there is an ambiguity in the parameter k, and you and I might choose a different k. So there is a one parameter way of different, one parameter, different ways of doing it, labeled by this integer k, but this will come back if we try to shift theta by 2 pi. So naively shifting theta by 2 pi doesn't do anything, but if we couple it to background field we see that it does do something. It shifts this counter term by 1 unit. So the correct statement is that the system with theta and k is the same as the system with theta plus 2 pi and k minus 1. So as long as we don't turn on A, it makes no difference, but if we turn on A, it makes a difference. Now let's go back to the next step here. So that was a refinement of this statement. So when we turn on background field, this statement is not quite right. We have to add k. There is still periodicity, but the periodicity is more subtle. We shift theta, but we also need to shift k. Now let's go back to theta equals pi. If theta equals pi, why did we say that we have the symmetry P? Because we had the symmetry P because P maps theta to minus theta and it pi maps it from pi to minus pi, but then we use the periodicity to bring it back to pi and that's why we have the symmetry. But now we see that this is not quite right because when we shift theta, when we perform P, this charge conjugation symmetry on theta, it flips the sign of theta, that's okay, but now we want to bring it back to pi. We need to shift theta by 2 pi, but that's no longer a symmetry because it shifts the value of k. So the lesson of all that is that P, the way we define it, is a symmetry of the system if we do not turn on background A. But if we turn on background A, it's not quite a symmetry of the system because what P does, so if we act with P on the system, so it shifts theta, then we can undo the shift of theta using the periodicity, but then we have to shift the value of k. So when we perform P on the action, the action is shifted by one unit here. So the action is mapped to the action plus the interval of A naught with coefficient 1. Okay, so somebody could say, well, let's try and fix it. How can we fix it? Imagine we shifted here by putting a half here. If we put a half, we'll define something else. Times will be changed, et cetera, et cetera, but in the end the shift will go away. But the problem is that we are not allowed to add such a counter term. K has to be quantized. So if k has to be quantized, we cannot fix the symmetry by adding a half integer at this term, linear term with a half integer coefficient. This is the hallmark of an anomaly. An anomaly is a statement that we have a symmetry, in this case O2, but when we try to couple it to background fields, we somehow fail. I should pause here and clarify something about the terminology of anomaly. And this is a sin that was performed in the 1780s. There are three different things that go under the same name and cause a lot of confusion. One anomaly, which first appeared in three gauge currents, say we are in four-dimensional field field, three gauge currents, they tell us if such a thing exists, it means that the system is inconsistent. So we are not going to discuss that at all. The second thing, which is called anomaly, this is what pi zero decays. This is one global symmetry current couples to two gauge currents. Still the same triangle diagram, but on one side we have a global symmetry current. If this is non-zero, this anomaly means that the global symmetry is not there. The system is still consistent. There is nothing wrong with the system, but the global symmetry is not there. And then there is a milder thing, which is also called anomaly, not to be confused with the others, which is what we see here. And I think a proper term for that is a tuft anomaly, because he wasn't the first to study, to study, but he was the first to made a lot of views of it. And this is the statement that we have some global symmetry. So first of all, the system is consistent. Number two, no problem with the global symmetry. The global symmetry is there. But if we try to couple it to background fields, the effective action as a function of the background fields is not gauge invariant. And that's what we see here. So what we see here is that the theta equals pi, there is a global symmetry, o2, but we cannot couple it, but it has, but it suffers from a tuft anomaly. It's really nice that this elementary free quantum mechanical system exhibits such a subtle phenomenon, and I will see what we do about it. And then later in the series of lectures, I'll use the same understanding in more complicated system, which cannot be analyzed so easily. Here it's so easy that you might say, oh, who cares about these fancy words? I know what the system does. So anything to the right of this line can be taught in the first quantum mechanical, the first course in quantum mechanics. It's nothing here that goes beyond the first course in quantum mechanics. Yes? Okay, so event that I'm glad you asked that. So people often say that anomalies have something to do with quantum field theory, and they have something to do with divergences, and they have something to do with fermions. Yeah, okay, so here is a system in quantum mechanics, not quantum field theory. There is nothing divergent here. In fact, the system is completely solvable. We have the complete solution of the system on the blockboard. Hamiltonian is diagonalized. We can compute all expectation values, and there are no fermions. And yet there is an anomaly. Okay? You're not disputing what I said. You just said that somebody else said, there is a whole confusion in the literature of whether anomalies are ultraviolet phenomena or infrared phenomena, or they come from this or come from that. I don't even know what's ultraviolet and infrared here. It's all trivial, and it exhibits the anomaly. And you can see it in many different ways. One way is just computing the correlation functions, the relations of the symmetry generators here. They don't satisfy the correct algebra. You can redefine then such that they satisfy the correct algebra, but then you need to go to the double cover of the group. And you can couple it to background fields, and you can see that the response is not right. Well, that's kind of overkill because in the classical system, we don't have theta at all, and the whole thing comes from theta. So in the classical system, we don't have theta, and therefore there's nothing to discuss. So yes, it comes from quantum mechanics, and it comes from the subtle object theories theta, which is... That's correct. But it's more than our run of bomb because it combines with this Z2 of charge conjugation. Well, we'll compute the path in a go soon. But yeah, there's nothing wrong. No, it's... Well, it's so simple that... So in the first course in quantum mechanics, you learn everything here, right? Menom and the wave functions, and you act on the wave function. So up to here, it's really elementary, here it's slightly... So as we move to the right, it becomes less and less elementary, but I think it's still quite elementary. So let me demonstrate it differently. Let's take the system to Euclidean space and turn on nonzero a. So if we turn on nonzero a, the only thing which is gauge invariant is the integral of a. So imagine time is compact. So we put the system in Euclidean space and we compactify it on a circle. And the only thing which is gauge invariant, so when we say a coupling to a, that's more complicated than necessary because only one number is meaningful here because we can always do gate transformations. And we can call this mu. And this is identified with mu plus 2 pi because the gate transformation is taking us around the circle, maps it like that. Okay, so that means... So what do we compute when we put the system on a circle? So on the Euclidean circle, what does this thing compute for us? Yeah, I heard the right answer. So it's the partition function or the trace over the Hilbert space e to the minus beta h, h is the circumference of the circle and we can put some chemical potential for this mu, mu mu, something like that, depending how you define things. Okay, so we compute such an object. So let's see what it is for our system. So since the system is completely solvable, I like to say, there's really no excuse to compute it. So let's define that z. And for simplicity, let's just be interested in the ground state because we can write the sum of all of them. This is not going to change what I'm going to say. So we're long looking at the ground state and I'm going to suppress various factors. So this and I'm leaving myself only through the ground state. Ground state. So there are two states there, the n equals zero state and the n equals one, which gives me one plus i mu. So these are these two states, the state with n equals one and the state with n equals zero because n is the charge. The charge is n. So this is the state n equals zero and this is the state n equals one. So going back here, we can see what really happened. The u1 symmetry multiplies the state. I wrote it somewhere here. The u1 multiplies the state by, oops, I forgot an n here. Sorry about that typo. The u1 symmetry multiplies the state by e to the i n alpha. So the charge is n. The state has charge n. So this is the state with n equals zero. Becomes the generate with the state with n equals one. So we see that when we act with charge conjugation which tries to map one to minus one, that's not going to bring us to the other state. The symmetry that really does the job here is a different symmetry. We needed to define it over there. There's a symmetry that maps n to minus n plus one and as we keep moving, we need to define this symmetry a little bit differently. And we see it here. We had two states, one with charge zero and one with charge one. They happen to be degenerate, but these two states are clearly not related by this charge conjugation symmetry. They don't have the same charge. So what are we going to do about that? Option one, say the charge conjugation is not a symmetry. That's option one. That would be too drastic. Option two, so option one, say the charge conjugation is not a symmetry. Option two, we take this partition function and define a partition function prime, which is e to the minus i mu over two times the old z. And that would tell us that we have minus i mu over two plus e to the plus i mu over two. Now, this charge conjugation symmetry is this. Yeah, this is all the theta equals pi. So I have, what do I, this is also, so option one is to say, the state, there's a state with n equals zero and the state with n equals one. They happen to be degenerate, but they're not related by any symmetry, so don't confuse me with charge conjugation. That would be too drastic and we're going to miss a lot of physics if we do that. Option two, that you will often find in the literature, say, well, let's multiply the partition function by this factor. We multiply by this factor, we say we have two states with charges plus and minus a half. Now they can be combined into an O2 because they have the opposite charges. So that looks good, but we can't have charges which is plus or minus a half. The global symmetry is U1 and our normalization was such that we only have integer charges. So what we need to do with this option two is go to the double cover. So option one, we sacrifice P. Option two, we say we thought the symmetry is U1, but in fact we have to be in the double cover of U1. That's also a little bit unsatisfactory. We have a system that had a global U1 symmetry. We try to couple it to U1 gauge field A and we get an answer which is like that. It's not seen variant. Option two, we get this answer, but this answer is not invariant under U1 gauge transformation. Under U1 gauge transformation, mu is shifted by 2 pi, so this thing will get a minus sign. So the partition function gets a minus sign under U1 gauge transformations. So we might think that's not a good solution. Both are valid. We can declare that the system doesn't have P or we can say that we have to go to the double cover. Both are valid solutions and various systems really realize, physical system realize one option or the other. We'll need to know, go very carefully, check which of the two options is the right one. Yes? On? You can compute it. It depends through, we'll have to go through the canonical transformation, but it definitely depends on this one because this is just an add-on. The other thing is that that would be the new P, etc. But we can work it out if you want. There's a third option and the third option, that's typical of anomalies, there are various things we would like to have. We wanted to have this O2, so we failed, so either we went to the double cover of the O2 or we throw away the Z2. These are the two options we discussed. And there is a third option, which is also interesting. We saw that the only problem was that we can trace back the problem is that this coefficient K had to be an integer. We said that we could fix it up if the coefficient could have been half integer. Then we would have said that there is no anomaly. An anomaly is something that you could have tried to fix by adding a counter term, but the appropriate counter term is illegal for some reason and therefore you cannot fix it up. But there is a third option. Say that our system, and it's always the third option, is that you relax the only assumption that was not yet stated. This is a general rule in life. When you are in a problem, there's always a hidden assumption that you forgot. Do you know what the third... Can anybody guess what the third option is? One assumption I didn't bother to state explicitly. Okay, see that everybody knows. So a system we thought is quantum mechanical and therefore it has only one dimension, zero plus one dimension. But instead our system is two-dimensional. If our system is two-dimensional, then we can solve the problem. We can preserve all the symmetries. So this is our Euclidean time that was compactified. Imagine we attach a surface to it. Arbitrally complicated surface. So we knew that if we only could add a half integer here, we would be in business. But we couldn't add a half integer here because that would not be gauge invariant. But we can add a half integer if we write it as what happens in the bulk. So add, so call that m2. So we define an m2 and add to the action. So the action was originally an integral d time of the Lagrangian. And now we add to it right the same s plus instead of that, I'm writing a half f on m2. So that's nice and gauge invariant. But it depends, I need an i because I'm in Euclidean space in this discussion. So that's nice and gauge invariant. But it depends on f in the bulk. So we had a system that didn't have a to begin with. Then I made it slightly more subtle by coupling it to an a. That allowed me to detect the problem more clearly. And it looks like all it depends on was what a does on the line. This formulation of the problem did not have any manifold attached to it. Now I'm attaching a manifold m and I'm adding this term. Now the problem is solved because I effectively added this half integer term term with k equals a half. The price I pay is that the answer depends on what a does in the bulk. So you often hear the statement and you will see it later in this series of talks that you add another dimension and then you work very hard to make sure that the answer does not depend on the added dimension. Here it does. When I wrote this term so that's an aside before that we could have written the integral of k with a. Things were one dimensional. We could have written it as k in integral of f on m2. But if k is quantized the things are independent of what a does in the bulk. Because how do we do that? This is a standard trick in this game. We add a bulk. We extend a to the bulk in some way. Now you choose a totally different bulk. So in this case it would be not a Riemann surface with one handle but it would be a Riemann surface with two handles. And you will extend your a the same a in a different way to the bulk. So we are going to form a new manifold which is the combination of the two. So my manifold was this one and your manifold will be this one two handles. And the difference between our two answers will be e to the i in integral of f on the combined system. So the difference between us will be e to the i k in integral of f over this whole manifold. But the integral of f is always 2 pi times an integer. So that's always plus one for quantized k. So before I went to option 3 I could have said that this term can really be thought of as extending a to the bulk but it doesn't matter how we extend it to the bulk provided k is properly quantized. Now I say, well I need something head to give because we had this anomaly. So we extend it to the bulk and now things do depend because it's not properly quantized. So you and I are going to extend it to the bulk differently and then we compute this thing and now since k is a half we're going to get plus or minus one. So with this way of defining the system so we're still in option 3 now it depends on the extension so z the partition function will have plus or minus sign but that's okay because this plus or minus sign depends on how we extended it and we knew that something had to give so that's what it is. In other words we have a quantum mechanical system that has an O2 symmetry this is the system of theta equals pi somebody asked me before only a theta equals zero none of these problem arise we have an O2 symmetry, no problem a theta equals pi there is an O2 symmetry but when we try to couple it to background fields we couldn't quite do it but we had various ways of dealing with it one say okay we can't do it we can't do it, that's the end of it or we sacrifice one symmetry or we sacrifice another by going to the double cover or we extend it to the bulk and the answer depends on the bulk. What I've demonstrated here is a very, very common thing except that here it's really was boiled down to this is almost a simpler system there is a simpler version of this with fermions in one dimension but just as you always hear that anomalies have something to do with divergencers and quantum field theory also here they just have to do with fermions so I thought I would present a system with bosons which looks like nothing can get easier than that to conclude just to extend it to a bulk we extended it to the bulk in such a way that for a closed bulk we have a closed bulk the partition function that we compute with these added terms it's not a partition function just the value of this added term is completely O2 invariant when we have a boundary it's O2 invariant but depends on what the fields do in the bulk when we have a boundary it depends on the bulk it's not gauge invariant it's not invariant under this Z2 but the mistake in the O2 the lack of invariance is exactly canceled by the fact that the boundary theory is not invariant under the Z2 so we have an anomaly in the bulk we have an anomaly on the boundary and the two anomalies cancel each other so that we have a nice invariant system in other words the system of this quantum mechanical system at theta equals pi just one dimension attached to a bulk where in the bulk we have only classical fields classical fields with half unit here a background field with half unit this is what also called theta equals pi but that's a different theta so I do not want to use this terminology this system together is invariant under the O2 symmetry but each separately is not the anomaly in the quantum mechanical system is canceled by the anomaly inflow from the bulk are there any questions? depends on the topology of the bulk the topology and the bundle that you pick on the bulk but not on anything else so if you make small deformations of A in the bulk change the metric of the bulk a little bit it drops out so it's a very mild addition so when I modify the system by adding the bulk I've changed it in a very, very mild way but it is important that I had to change it no, it depends also on the first-term class, you raise your hand with math yeah, so it depends also on the first-term class does this answer your question? you said that different physical systems would employ option 1 or option 2 does option 3 capture all of them or will it not be able to capture some physical? so in a physical system it depends on what the physical system is so, for example the physical system might actually have a bulk yeah and it might actually have the full auto symmetry and it might have the bulk and then it will use option 3 the system doesn't have the bulk something we'll have to give so either you say that there are two states at theta equals pi which charges plus or minus one so charge conjugation is a symmetry but with u1 we had to go to the double cover that's extremely common and this is how you usually get fractional charges of various particles or you say, no, charges have to be quantized symmetry is u1 without going to the double cover but then we don't have charge conjugation this can also happen but it's important to know the menu of options and when you use one which one you use and not do half the system one way and half the system the other way because that would not be sensible yeah, it's actually quite common it could not matter people they don't present it this way but they do exactly this in systems that are actually in a way simpler and in a way more complicated than this so if you vary theta smoothly to pi is there anything special in the gauge group in this case it's not a gauge group it's a global symmetry we are only talking about global symmetries the system has a global symmetry of the global symmetry it's convenient for us it's a tool to couple it to a background field and once we couple it to a background field once we couple it to a background field we would like that global symmetry and that's what we run into trouble but the trouble that we run into in coupling to background fields is identical to the problem I presented here without ever mentioning background fields so it's a matter of taste whether you would like to set A to zero and study the operators more carefully and see whether the relations in the group are satisfied or not or to say we need that or just add background fields in keep track of all these subtleties using what happens with the background fields I don't know if I answered your question but the answer is A question enhancement of the group not the gauge group but the group there's no enhancement but from U1 to O2 or from SO2 to O2 yes that's a property of the Lagrangian is that different if you vary theta towards zero or theta towards pi yes, completely different because in both cases the group is O2 but in this presentation theta equals zero we had O2 on the nose theta equals pi we found the central extension of the O2 I don't know if you want to call it enhancement or not there's one more element either we have to double the range of alpha the parameter or we say that where did I write this comment here or we have to add this central element so it's up to you how you want to describe it but you have more element it's not a bigger symmetry it's a central extension normal questions am I done? I have four more minutes I've just finished the first 15 minutes in the first lecture so I'm going to change topic and I think this quantum mechanical example was worth presenting even though I will probably because of lack of time present much less than I planned because I can assure you that later on in life you will see this adding the extra manifold say that our space time is really the boundary of something else and to discuss the anomalies what happens in one dimension more or using this in various context for example, example 3 is what is known as a topological insulator although the connection might not be obvious at this point but I think this was useful so the next topic I want to talk about is moving to quantum field theory but it will be topological quantum field theory and I would like to make some introductions to transimons theory because we'll use it later who here has ever studied anything about transimons theory about half and I know that you haven't ok, so for simplicity so I'm changing gears and I will have a u1 gauge theory in three dimensions and I'll denote the u1 gauge field by b so I have a u1 gauge field and when we say it's u1 it really means that on every close two cycles that's in 2 pi z so all the fluxes are quantized and we can write an action so my convention is always that the action is like this and the actions since I've been in euclidean space will be i k over 4 pi integral bdb so this is the transimons action but to properly define it first similar to what we had before except in one dimension it's linear in the gauge field and here it is quadratic in the gauge field and one way to write it so this is a three manifold so call it m3 is to write i k over 4 pi integral db db on m4 where the boundary of m4 is a three manifold m3 so we take our three dimensional space time we extend it to a four manifold we extend the gauge field b to the bulk and we compute this thing in the bulk so this is nice engaging variant but we have to check that it's independent of what happens in the bulk so again the same story we had before this is our m3 and we can extend it to the bulk one way or some other way so this is m4 this is m4 prime but with the opposite orientation so you and I picked a different m4 different four manifold and we extended the gauge field differently how do we check whether it's independent of the extension we construct a four manifold which is the union of these so now it's perfectly smooth there is no boundary perfectly nice manifold so we compute this thing on the big thing on the whole thing so that gives us an answer and this is a good definition for the three dimensional theory if the partition function or this thing is independent on the closed four manifold is independent of the extension it's not even a partition function this has to be exact configuration by configuration in the functional integral so we're doing the functional integral over little b we extend it to the bulk sure it's independent of the bulk and the condition for that is that k over 4pi integral db db for this whole thing I'll call it m tilde 4 which is this whole thing four dimensional manifold this should be in 2pi times an integer and if that's the case it's independent of the extension it turns out that the answer depends on some properties of the four manifold correspondingly the three manifold if the four manifold is a spin manifold is a spin manifold and we choose a spin structure for it then the allowed configurations are restricted and that would tell us if it's spin that k is an integer if it's not spin if it's not spin then k has to be even so we'll see in the discussion that depending on there are two, the discussion will bifur k, depending on where the k is even or odd if k is even we don't need to choose any spin structure and so forth and if k is odd we do have to choose such a spin structure that's a tool so if it's non spin there are more options and if there are more options there are more restrictions on k and k has to be even so whatever I can do I'll do in parallel for the two cases and when the discussion bifur k I'll split to the two separate cases how much time do I have thank you


Welcome to the drum history podcast. I'm your host Bart van der Zee and today I'm joined by Bill Cardwell of CNC custom drums and Gladstone drum shells. Bill, welcome to the show. Thank you very much Honored to get to be on your podcast. It's it's an honor to have you here This was actually a request from a from a listener So this is really cool that we get to do this and and honestly the show is typically like I think I told you before it's about like Leedy in the 20s and all this stuff and and you are a little bit of a newer company But you were just telling me that it has a lot of vintage heritage. So I'm excited to learn about this Why don't we go back to the beginning and just like I said to you before we did the interview I don't know much about the history of CNC and Gladstone drum shell So why don't you take it from the beginning and and teach us about basically your history and on these into the two parts of your company? Well, let's do that. That would that would be very easy for me to do I worked for a Then a 14 billion dollar a year corporation and the chemical industry and Didn't like it a whole lot, but I I would play the radio all the time And I would listen to talk radio talk radio was big back in the other we're talking early early 1980s and this guy I was listening to this guy on the radio and He was talking to a caller who wanted to do something to make some extra money I was wanting to make some extra money because I wanted to buy a new PA system for my band back then when you had a band you had to have your own PA system and And sound man and everything when you set that up and played so I was trying to make some I wanted to make some extra money, you know, because you know, there were kids and everything else and Life to take care of so this guy goes What do you love and what can you do? Because this caller was fishing. Yeah, and so I got to thinking and I go well you love drums and You like fiddling with them. I'd always my very first drum set when I was 15 was a gold sparkle Rogers drum set and I was always messing with it and I'd had a Ludwig acrylite snare drum since I was 10. So I was always fiddling around with it Anyway, I'd really really loved a Really loved tinkering with drums that being said I'm not what you would call a mechanical type person I can't build a square box Total impossibility anyway, I started I put an ad in a Little paper called the thrifty nickel and it said cash paid for used drums And it had my beeper number on it. This was the days of beepers and I Kansas City was rich with old drums just back in the 1920s and 30s. I mean, there's so many Duke Ellington came out of here and So so so bird bird was from here and and it was just it was just a hopping town when they talk about 12th Street and Vine that was where all the action was and Why we even have a line called 12th and Vine, but So I started just getting drums and fixing them up and selling them and getting drums and fixing them up and selling them and I was doing this out of my Family room downstairs in the house and in the garage and Before I knew it. I had like accumulated a double-car garage worth of stacked up drums from all eras and I drove out Probably about an hour from Kansas City and this guy had a big old double-bass pearl Inexpensive drum set with some cymbals and stuff and he wanted $600. I go man You got anything else here and he said yeah, I got this old broken-down drum in the closet he went over to his closet and pulled it out and It was the first time in the world I saw a super sensitive with the snare wires underneath the top head and underneath the bottom head of Ludwig black beauty and I said we'll throw that old drum in I'll give you 600 bucks and so I didn't have any idea what I was even looking at and I Went to a music store here in Kansas City and the guy immediately offered me six hundred dollars for it Well, 1980 somebody's offering you six hundred dollars for broken-down old drum Something's not right. You know didn't add up. Yeah, so I passed on the deal and I Started doing some research and found a found a guy by the name of John Aldridge. Oh, yeah, and John Aldridge I think is the guy who did more for the inception or the popularity of vintage drums I Started talking to him on the telephone found out a lot of stuff From him and we've kind of kind of went from there so to speak And then I had already had a lot of knowledge on shell construction and such from you know going and buying these old drums I would go I Mean I did silly stuff like went to a went to a guy's trailer that was out in the middle of nowhere and He wanted 20 saw my ad and he wanted 20 20 bucks for this drum set Well, it was a 1952 Gretch green sparkle 2213 16 with 60s Ludwig wooden snare drum on it Covered in aluminum foil, which I found out was mod orange when I got home You know just crazy stuff like he went 20 bucks because he had mowed a woman's yard and she didn't have the money to pay Wow, and now so Yeah, I mean just crazy stuff like that was happening and there was no such thing as vintage drums at that point in time Modern drummer came out and not in my world and there was there was a small cluster of people across the country That it was like it's some way. We all seem to find each other You know and and and mostly it was through John Aldridge I know I got this call from John one day and it was this guy named Rob cook and Rob called me and he said John Aldridge told me to call you because you can answer the questions that I Have about vintage drums and so I go, okay now Like I said, this is even pre cell phone.  Hey, I've got that. Hey, I've got this I got I had the honor because I had a color printer in the office that I worked out of it at Bayer I Actually printed the very first color not so modern drummer That's so funny John John has been on the show before and has told a little bit of the other side of this from his Perspective and I think he he actually mentioned you in that episode and talked about that So it's it's funny to hear it come from you as well And he mentioned that his wife was like they were in marriage counseling because of this in the phone bill and the constant Discussion, so that's that's hysterical. Yeah, and he I mean to me. He's like the godfather of vintage drums that people don't really know about or appreciate what what he did for it for them in the day and and a Lot of it has comes out of this baby boomer generation that I'm a part of Because these were the drums from that we saw when we were kids Usually we couldn't couldn't a lot of us couldn't afford them and then Grew up and I was probably somewhere around 29 30 years old Maybe a little older than that, but you know early 30s at that point in time, so we were we were you know We had a desire then for the things of our youth that were were gone And I'd totally quit playing drums and which was something else that seems to be a reoccurring theme among My generation we went on we got our company jobs We did our thing and then all of a sudden, you know, we've been away from drums all for eight or nine years And it's like and I want to play the drums again So I'd gone out and bought a new Pearl drum set and it wasn't really You know, it wasn't the sound that I wanted. Yeah, so you so you end up you end up going through this process and Over the years Vintage drums went from this neat little club to this huge huge huge huge amount of people and the original C&C was a guy named David Carrington and Bill Cardwell and David wanted to build drums and we ended up doing a retail store because He had so many vintage drums and I had so many vintage drums and they were Overrunning houses are both of our houses. So we we just got a store front and and started selling sticks and heads and used and vintage drums out of out of the store and He wanted to start building He also Started a family about that time, but the first drum set I got to build I built out of with Keller shells I built out of my my garage I had shipped a three pallets of Drums to a gentleman called named Palo Spirallotti in Italy that Ludwig eventually did a book called the Palo Spirallotti collection and all the drums in the book except for Ian Pace's Made in Japan kit and Cozy Cozy pals red sparkle Ludwig kit all the other drums in that that book came out of Kansas City out of people's basements and garages and Whatever from over the years so Did just got to be Something that There were so many people involved there wasn't the cool little club anymore I I Don't want to say I lost interest because I've never lost interest in In old drums. It's just that I started wanting to I started messing around with a router on a router table and if an old vintage a vintage drum had an extra hole In it back in say 1990 1991 to three nobody even wanted it You couldn't give it away. Oh, it's got an extra hole. No, they all they move the realm out. No, I don't want you know None of those things were really They didn't retain their vintage value at that time because there was so much Pristine stuff out there and you could buy it for nothing so I Started messing with the shells that had been Bastard eyes so to speak to where I thought okay if I was building this drum And I wanted to get the sound out of it So I just started messing with the bearing edges on Vintage drums that I couldn't sell and retrospect I wish I'd left the darn things alone, but it's it it did give me a it did give me a lesson and how the edges were then yeah the shell constructions of all the different drums and and All of that but Paolo Paolo Spirallotti Did interviews and wrote for magazines then he had Karl Palmer of Emerson like and Palmer at His house and he was doing an interview and the I don't know I think it was like three pallets of vintage drums Showed up while they're doing the interview and all of a sudden you know they're in their tearing boxes open and Seeing what's come from the United States and Karl said I've always wanted a drum set in my sizes that Looked like Gene Krupa's kit from the 1940s but had gold hardware on it and And Paolo said call my friend Bill Cardwell. He'll make it for you and wow so I Start getting these telephone calls and this guy in a British accent that was a little bit higher pitched than me You know saying this is Karl Palmer and I'm going yeah, I'm buddy rich You want to go to Pizza Hut and have pizza, you know, it's like I thought it was one of my friends just messing with me and I did have a fax machine at home and that's the way Paolo and I communicated and Finally, I get a fax from him telling me you stupid idiot Karl Palmer's trying to call you Will you talk to him when he calls and quit hanging up phone? so The very first drum set that I got to build was and I and I use Keller shells and I made it with a Six-ply maple With six ply reinforcement rings it was white marine pearl I had a bunch of old Radio-king hardware that was because it wasn't being reproduced back in that time but I had a whole bunch of old radio-king hardware and I went and had it gold plated and And basically built Carl a double-paced drum set to his specifications and That kind of opened the door for building drums and My partner David he wanted he was really into it Well, he was also starting a family at that time too and by the time We started building drums out of the back of our store in a little room that was about 12 feet long and six feet wide He he got busy with family and he was He was an engineer and he ended up Me buying him out and he ended up moving to Dallas and he and I are still great friends to this day I love the grout of death and So we don't have any of these It was it was not a bad thing But we were just we just build a set in the back of our store and set it up on the floor but when I saw that the big boxes were all coming to town and everything I got sold stores was offered early retirement from Bayer Chemical Corporation and and And and it just seemed like everything was lining up to To start making drums now I had four artists at that time I had a grand total of four endorsers which Wasn't much made on by then. I had I had five I Forgot we get we'd picked up sparkle horse, which was a great pickup, too so we had anyway, we had we had five drummers and No potential for selling any more drums now. What year is this at this point? That by this time we're looking at 2003 oh, okay We're we're all the way up to April of 2003 and now let me ask you was Carl Palmer's set Was that technically like the first C&C drum set? It was it was I Didn't there's There's not any badges some I thought I got it You know what I got a picture of that drum set about three weeks ago It's a first. I didn't even take a picture of it when I made it. Oh, wow Didn't think anything about it and so I got a picture of it the other day And I can't remember what I did for badges on it I don't even think I did badges on it or maybe I don't know can't remember Can't remember but it was it was the first drum set I ever made so not bad so yeah, kind of It's kind of tough when you start there, isn't it? But we would I built a we would build a kit and we would put it in our store and we we took one to the Chicago show Early on I think it was the second or third Chicago vintage show We took a custom David and I took a custom built drum set and I and it I remember it had a 7 by 13 Wooden snare drum on it and all Aldridge came he kept coming over and playing that snare drum and he goes Why does this sound like a metal snare drum?  Yeah, it sounds like it is it is the only way There was now as I look back on it. I should have had better plans, but I didn't have any plans. I just This was kind of flying by the seat of my pants Sure, and we had a major drum company at that point in time excuse me in 2000 they were interested in What I was doing with building drums and So I thought we were gonna do something with them I'm not gonna get into that. Yeah, it was it didn't it didn't pan out And I was kind of forced into a situation of like gee. Well now what are you gonna do and We just kind of Made it along, you know one day to the next and I mean I would literally build a drum set My son was on tour and he was on like shore records then and had to do a European tour so we built a drum set and He took it to Europe. I said leave it over there We get any we get any more artists We're gonna need we're gonna need backline drums for you know, I'm already thinking about backline drums and don't even have orders We're gonna need it for our artist one of these days and he did They don't and that gets stayed over there for years and years and years But we reached the point where we couldn't make the shells Keller makes great shells. I don't have anything against their work at all in fact After us making shells, I have more respect for what they what they have done over the years but no one was making shells like they made them back in the 40s 50s 60s and early 70s and that was That was kind of my point of reference of what I wanted to be able to produce as far as drum shells were concerned so it was Imperative to get drum shell molds in here to to make drum shells to get those sounds and Not to make replica drums, but to make drums to the specifications of what those shell constructions were yeah and When we did make them then to And the these machines are so much better than the equipment that they had To use back back in the 1960s So, you know, it's it's not the same as an as a 1966 psychedelic red Sparkled drum set that the edges have been all beat up on and still sounds great Yeah, you know, it's built in honor. So to speak of those drums and hopefully they'll have the longevity that They're still around 50 years later and people want to play them too. Yeah And now so this is Gladstone drum shells, correct Which right which I think you were telling me before that you did sell them as drum shells at one point But then it got to be too crazy because I think we're getting there But C and C has just blown up in popularity and it sounds like that's right at about the time in that mid 2000s where we're at but and Gladstone is named after the town We're yeah, we're in the town of Gladstone, Missouri However, when I was 10 years old and my mom traded in her French horn that she had played in high school and got me a 1966 acrylite snare drum and they just came out with the uf they I think they call them UFO cases now, but that 66 acrylite and It had a practice pad on top of it It had Billy Gladstone's name on it Because he and had been at the Billy Gladstone and had invented that practice pad and so the patent a Ludwig. That's great so I would have to practice of course with With my practice pad on because no one had wanted to have to have to listen to the snare drum and Me trying to learn to play it. So there was that correlation and then My store was in Kansas City but if you drove six blocks down the same street all of a sudden you were in the small township of Gladstone and I found an industrial building and it's just pretty much an empty concrete floor and space and we built the We built a drum building facility that Placed off of how we build drums. I mean, we've just kind of winged it. We've winged everything along the way Yeah, and I mean we've never really advertised We you know, we ask our artists to keep the C's on the bass drum head That was one thing that we wanted they they I've learned to tolerate and be okay with the fact That the C's aren't always on the head. That's my My my problem because you know, they do change bass drum heads for some artists Don't want branding on their stages and all these different things So I've had to grow out of that Speak but it literally this company has grown on the back of our artists They have been responsible for what we've done over time and a lot of the ideas that have occurred have occurred because Artists now like that the player date line. We knew we wanted to do it and We didn't know exactly how we wanted to do it But we had two artists to it asked for a center lug kit, you know And and one of them was made with a maple shell I mean both of them were made with maple shells and then I got a call when we had we started We had started working with a gentleman named Joey Wanaker and Joey called me one day and said hey I I picked up this old majestic kit and it just sounds so great can you make me a set of shells like these old majestic shells and and Which were blue on shells and so we went about you know finding the right wood to make those shells and we made them they were so musical and So nice, you know coming out of modern-day machines and not being made, you know like Like they had to be made back in the 60s and yeah and early 70s when they were being made. I mean the technology Hope that I hope that shell too, and it's just you know, totally. It was just it was just great and Jake and I worked the better now Now we're all the way up to 2011 Jake and I worked just about all that year on Coming up with that player date one kid and so when we built that thing and We managed to get it out to the NAMM show and we built a few other a few other shells But I got when we got on the plane and we were flying out the net NAMM show That year I said, you know and when I think we were offering them in three colors And I said, you know if I can sell 25 of these because I'd quit going to NAMM shows because we were a custom company Yeah, we would we would we would build everything Fill up a booth. We'd sell everything in the booth. We wouldn't take any drum orders. So basically it was you know, I Don't know it wasn't It didn't I didn't need my ego stroked I was past that by that time but the The player date ended up being a drum set that we we ripped off the 60s scratch edge on the shells Which was you know, one of the things that Jake jigs IDs that hey, let's try these these full contact edges And so we did that and and he took them out and played them on a few gigs and stuff and yeah And we messed around with that. So Jake's always Jake's always been a guy who's who had the ideas and I had Ideas and we'd put them together and when they would mash and they would make sense You know, we would usually have something that was doable. So this is so cool And that's card. Well, who's your son obviously too, right? Yeah, that's great So I went out there and I think we sold like 60 something player that took orders for like 60 something player date kits But when I was when I was on the plane on the way out there. I said if I can sell 25 of these I mean I get back to Kansas City I want to try maple on the outside and maple on the inside and and leave that luon in the middle and See if I can come up with a drum shell that's going to be different in sound but still going to have that more of that vintage sound to it and Give me another line of these well when we sold the 67 we had to focus on building those and Getting those to stores and hoping they so because it's one thing to take the orders and sell one order of them You know out the door Yeah, it's another thing then to get reorders. Yeah, so As soon as we got them out the door, I said hey guys, I'd Notified store owners. We got a new drum shell. It's called a player date, too And I didn't even tell I didn't even tell the guys when I thought when I thought of the maple I didn't tell them that we got back to Kansas City So they didn't tell anybody else because I don't think maybe there was you know I don't think in 2011 and or January 2012 Anybody was doing anything with a full contact edge at that point really well No, I mean it was not I don't you know, I may be wrong, but I don't know anybody who was doing it I think everything was much sharper. The bearing edges were a lot sharper at that point Oh, yeah, they were and and which I like too because it gives you a real Wide range too, but anyway, but I I no more got back and some another little drum company had had a already had a video on on one from the store in In The UK where this guy says me and so and so put our heads together and we came up with this great new edge and it was like He just that ain't a new edge That's the 60s crutch edge and you just saw it in my booth at the NAMM show two weeks ago So I just quit to go into NAMM show that in was like yeah, I'm not going I'm not going out there I'll just people can just find out what we're doing when we're doing it. Yeah, that's a common theme nowadays Yeah, so I just don't you know you just so I gave up on that but anyway, we've We do things that we do because I like those shells that he was that Joey was talking about and Joey has a phenomenal ear and I've had artists along the way who we've listened to and If you listen to these guys and the sounds they want and are able to reproduce the sounds that they want then Then it's then it's a value. Yeah, then it's worthwhile. Yeah, it's I'm a big fan of the old Mij the stencil kits as well like the majestic they I just think for the value you get, you know You can get a nice cool vintage drum set with amazing finishes and and they sound Great and the snares especially are amazing. So it's cool to know that that's kind of a part of your history as well a little bit Right well in everything back then was I mean through the 90s we were educated on More resonance more resonance more resonance more resonance and everybody was trying to build a drum that would just Resonate all over the place and go in thinner and thinner and thinner and thinner on the shells It ended up that there was a great number of people who wanted drums that didn't ring on forever I love a big full sound. Yeah But you know My son just to soon throw a tea towel over a floor Tom and play it as is not Exactly and everyone's using moon gel now and it has been for a long time But you get the drums that resonate forever, but then you Dampen them to get like that nice kind of studio, you know studio ring sound and so kind of redundant Yeah, it's like the the second drum set that we built for Ringo. We built Ringo a drum set and then he he didn't He wasn't he wasn't big on Drum construction, I mean, you know wasn't aware on drum construction, but why would he need to be you know? Yeah, he could play it. He could take a brand-new pair of Zildjian hi hats and make them sound just like when he's sitting there playing, you know in the 60 I'm saying inside of the stage. He's doing soundcheck. He's sitting there and I'm going How does he get the same sound he got out of those old? K symbols does he get out of that these brand-new I had yeah getting the same. It's him Yeah, it's him, but his drum tech is Jeff Jonas is Very and very knowledgeable about drum shell construction. It's extremely knowledge We built him a drum set and and he liked it. He liked the drums, but he liked the set that was built but he Got the impression from Jeff that I could make a drum set sound like whatever he wanted it to because Jeff taught him about Bearing edges and why his drums had sounded the way it did was another on drummer on tour Who had flown down? the front of house man from the guy that she had played with at the show that I went to in Chicago to find out why Ringo's drums sounded better than the drums that She was playing at that time and of course I told I told him because you're playing them and which he said That's right, but he was right man, you know, I just had Gary Astridge on the show I actually did the interview with him. Oh Man, I haven't seen Gary in 20 years out there. That's funny. I talked to him on Friday two days ago This is Sunday today and he talked about that about how Ringo Just anyone else could play it and then Ringo picks it up and it sounds like Ringo like it sounds There's there's no denying that. Yeah. Yeah, it's and and and that's what it was But he decided he wanted a drum set that sounded like When you played the let it be album Now you didn't want it sound like the drums on the that when he Live hit the drums on the let it be album He wanted a drum set that sounded like when you played the record He wanted the drums to sound like the record Gotcha.  They're probably not the same a lot of variables. Yeah a lot of variables. So But we you know and it ended up is like hey, did you use that natural maple kit that Used on the rooftop and video. Yeah. Yeah, I go look at the rooftop. He's got a towel over the floor Tom, you know so What what the edges I ended up cutting on that? Maple poplar maple kit ended up being what we Edges we use now in our 12th and bond kit. Hmm. So He he helped me out with those edges Wow, because that's that's the that's how I cut it And so I figured my hex is good enough for him. I'll be good enough for the rest of these guys too So yeah, really and I mean it's not like like I said before you were getting to the point where I mean You must be just thrilled that C&C has become one of the most popular, you know, kind of Boutique drum brands in the world. I mean you guys have just a very Like there's no other brand really like it. I mean you're it they feel vintage, but they're just The quality is just beyond apparent when you see them and when you play them So, I mean things just skyrocketed for you guys. Yeah, I mean how do you get the how do you know? You don't know.  I mean the artist or the guys that have I Haven't made C&C what it what it is as far as drums are concerned the artist have and and You know my maybe my desire to facilitate what they're asking for but A lot of these guys have just had the idea, you know And and we've got to do some cool cool things, you know that I never thought I'd get to do I mean I look I grew up in rural Arkansas On a gravel road and worked in a cotton field when I was a kid. That's my life, you know So the life that I came out of So it was like What's the chances of a guy? In Arkansas Who was seven years old when the Beatles were on Ed Sullivan ever getting to build one drum set for Ringo much less too? You know, yeah, that doesn't happen. So It's just there's been a lot of good dumb luck is all I can say Yeah, you've you've made it and and as we get close to the end here Why don't you tell people is there anything kind of cool you guys are working on? Now, I mean, it's it's 2020 right now Anything cool in the work. So you guys kind of just business as usual We're working on some metal shells that are unique and different that have a lot to do with copper and I love the sound of copper and the effect that it has so I've built several of those I think Memphis drug shop has some and a few other stores have some of those snare drums and Both the guys and modest mouse have them and and and I sent one to New York for Joey Wannaker to use on a Giggy had to do in New York with Paul Simon or something. I can't anyway And he said can I keep this and I'm like yeah keep it, you know why not wow so So we're those are something that we're playing with a lot right now. I think we're gonna Take the player day on a little bit Expanded and Offer some new things with it We just kind of like we still fly by the seat of our pants. Yeah It's just the way it's just the way things seem to go well, it's working You've come a long way from the you know The fields of Arkansas to be to be doing this now and brushing with the the greatest drummers in the world That's just really cool. It's kind of an inspirational story and it sounds like Passion is kind of at the heart of all of it of just And I like how you said to we're like you were out of it I mean you had a full-time Regular job you were out of it for a little bit and then you you came back and and look at you now So, you know, everyone gets that where they get, you know a little burnt out on practicing or life takes over and Oh, yeah, I was poor. I was 47 years old When CNC custom drums became an entity into itself Wow, so I didn't you know I thought at that point in time there weren't very many custom drum builders. I By golly, I think within a year after I opened up C&C custom drum. There's Many drum builders is there were convenience stores every everybody who Couldn't get a job ended up being a custom drum builder. I think yeah, so there's you know, so it's like I Don't know that there's a lot out there and there's a lot and there's people out there doing great work So I think we live in a special time of of drum building and and again Our community is really strong and and I think everyone has a lot of respect for what you're doing Just because you guys keep your head down and do your work and and produce great drums So I think now is a great time to tell people that they can check out CNC drums at C and C drums USA comm so that's C And see drums USA comm and I really want to give a quick shout out to Jonathan Webster who is the gentleman who reached out to me and requested this episode. Oh, yeah from Canada Yeah, so that's that's pretty cool Why are Canadian such cool people? I just are we They they just they're just I've we've had so many great Canadians that Play our drums that Sweethearts. Yeah, great people the neighbors to the north. So Thanks, Jonathan and and to anyone else out there who wants to to reach out and request some episodes That's always welcome.  Thank you. Yeah, this has been an absolute pleasure to talk to you and keep up the good work And we'll be in touch down the road. All right, great. Thanks, Bill. Take care If you like this podcast find me on social media at drum history And please share rate and leave a review and let me know topics that you would like to learn about in the future Until next time keep on learning This is a Gwynn sound podcast


Hi, my name is Chris Guter. I am a librarian here at Alden Library and I'm going to be showing you how to find the full Text of an article when all you have is the citation to go on Okay, so if you have a citation and you want to get the full text for that citation What you need to do is take a look at it and identify things like the author the Publication date and in this case the most important thing is to get the title of the journal So for this first article the journal is the Journal of academic librarianship. So what you do is You go into the library homepage You click on Alice change this to periodical title and type in the Journal of academic Librarianship Okay, so what we see here is we have two records the first one is typically the paper And the second one is the electronic resource. I'm going to go ahead and click on the electronic resource And what it does is it shows you the coverage and specific databases that we have now our article is a 2011 volume 38 issue one. So if I go back there 2011 is right here 1993 to present so I click on that Go to issue one And there is the article Futuring strategic planning and shared awareness and the PDF is floating right there Many go back here to the library homepage Now for the second one The author is Hagman date 2011 at the art the journal is called Public Services Quarterly volume 8 issue 1 So I would go back to Alice Periodical title search for public Services Quarterly and this case we only have it electronically and also we only have it from 2002 to the last To 18 months ago. So if I look at the citation again, it's 2011 chances are we don't have it But I'm going to double-check anyway. So that's volume 8 issue 1 I click on the link to the full text 2011 2012 volume 8 issue 1 and I would scroll down here till I find the one written by Hagman or I could go by title Should be something on Twitter Joining the Twitter conversation. So if I click on that title, I can then click on find it and We do not actually have full text for that article. So all I would do is go back to the library homepage click on services Borrowing and I have to do that, right? Enter library loan document express fill out a request and we would go looking for it and scan it and send it to you for free Always if you have any questions, all you need to do is click on the need help and you can call us text us email us You can chat with us live and that's about it. Have a great day


Most ecological efforts were all about philosophies, propagating philosophies. This is an ecological effort with a solid economic background. See, this is the important aspect of the Cauvery Calling, that it is an ecological project, but with a very strong economic basis. That is why it will be successful. Because it's an economic process, it will succeed and it has to succeed. So what is the biggest challenge in this process in your initiative? What do you think is the biggest challenge? See, the biggest challenge was the loss of revenue for the farmer for first three-and-a-half to four years. That was the biggest challenge. So this is what we first focused on and we focused on this and saw that a farmer gets a certain subsidy to bridge this gap of loss of income. It's not a hundred percent loss of income, it's a gradual loss of income. First year there is some loss, second year more loss, third year more loss. By fourth year it will start yielding, fifth year definitely it will start yielding. So now they have given 125 rupees per surviving tree and this is distributed on a yearly basis which has made the difference. Which is the bridge? That was a bridge that we could not cross by ourselves without the government support. Oh, that's right. But there are… even once your volunteers are there, they'll be constantly monitoring the situation, not just planting and going away. No. But they'll be monitoring. Yes, of course. See, above all the significance of this is, the trees are being planted in private land. That is, partially it is replacing the existing crops. So farmer is not going to let it die because it's a crop. See, we must understand it is called agroforestry. But I would like to change the terminology as tree-based agriculture because it's not about raising forests, it is about farming trees. The monsoons won't stop for corona, the farmers won't stop for corona, so how can we stop for food? So taking care of the saplings and taking care of our trees, that was the only concern. It's amazing how the farmers, the government and the volunteers stood up to make the impossible possible. So the vision is a very large vision for these two states. We had a lot of plans from nursery planning to outreach planning. In Karnataka, where we are stepping in for the first time, the awareness generation phase was the most important phase. When we were gearing up is when the corona outbreak happened. Then we started re-strategizing this whole program. We started surveying the farmer leaders and influencers. The kind of introduced us to is that the most preferred medium of communication nowadays with farmers has been WhatsApp. And second, it has been Facebook. Whenever we reached out to a lakhs of farmers through these internet platforms, what we saw is that there is a requirement for the farmer to speak to someone. Personally, to get their questions and doubts clarified. So we had set up a helpline number. When we talk to farmers, I mean, they are simple people and some of them just pour out their pain. But when I talk to them, they really like the enthusiasm. They say that, you know, if you are sitting somewhere else and you're speaking with each of us for 15-20 minutes, how can I not go and pick up the happening? The another parallel or equally important support that was happening was the support from the government of Karnataka. The forest department has done an exceptional job and a commendable job. They have been supporting us and they have been working with us for like a day and a day out. And they are supporting the farmers in every way. When we came across this problem in March, they would close the door and then open it. After that, the government announced the issues related to agriculture. After that, we started our production in the nursery. We couldn't go out of that. For another 4-5 months, they haven't gone home since the lockdown started. In Tamil, they call it the nursery. It is a matter of life. Every step should be taken care of daily. Even then, with the commitment of a farmer in the nursery, they are in the nursery. So, pandemic has no way slowed us down. Because of the pandemic, we were little hesitant that how will it work because will we be able to go out and do this work. But the dedication of our volunteers, risking their own personal health and well-being, they have been out there travelling, doing things. But above all, technology, media and the cooperation that we have from the forest officials and the agriculture ministry has made the difference.