Lecture 4 (first part only)

0:00 This is the second page, the third page, it is clear that there is an interest to see the transforms, to go through all of them, all the courses to be written.

2:30 So I will leave the first page, I will explain the locations. Look at the beginning. If you want, it's a little bit like if we had hieroglyphs. It's a little bit like that. It's something that is written in a text, that is written in a language that is all written. And what you have to understand is that this language that is three pages long, it's the wonder that we have, the most precise, that sums up your language. That is to say, when everything is composed on the language, you realize that it is mathematics. And then we will understand, we will rewrite the term of mathematics. And we're going to add a couple of pages here and there, because we're going to go through them one by one. The point is that what we're dealing with is a resume of the century and the century of the other half, the experience of the other half. And in addition, I want to say that the summations are based on the artists. Yes, of course. The others are the friends of the other half. Compact. They are the friends of the other half. So, what are the first terms that we have here? You see, the prediction A is what we call the gluons. There are 8 gluons that give the force P, which are geological bosons. The first term is the symmetric term for the gluons. We are in a geological boson called the Feynman's geological boson. As it is a geological theory, normally it cannot be degenerate. The quorum cannot be degenerate, it is just a geological boson. The second term is a term that comes from the English word for square, and F.A.B.C. is the structure of the constant for the group S.

5:00 So F.A.B.C. is not forces. The term is called G.S. which is the constant of force. It is the constant that governs the flow of the interaction. The term in F, A, B, C, F, A, B, E, G, B, U, A, B, etc. is the term in A power 4, which appears when we write the curve in the square. If you write the curve, the curve is D A plus A square, which is the difference in square, there will be a term in A power 5. The term in law, there is a term in G, S, square, which is the A power 4 term. The Q, Sigma, the Qs are the quarters, so Q is the collective number for the quarters. Cycloa is a symbol for generations, for three generations, and Y is a symbol for generations. The second line, the second line of the second line, with the letter RG, is the phantom of Feynman, De Ligt, Fabien de Corbeau. They are there to square the generation factor of the third line. After that, we have the big corona in the West. After that, we have the boson in the West, which is the boson responsible for the interlinear boson. That is, Fermi had written the interaction at 4... No, no, he had written the interaction at 4 carbons, which he had written in the West, because it was in the West. So people would have imagined that there was a boson called the interlinear boson, which is responsible for the interaction at 4 carbons. Because the dimension of Fermi is not in the West. So, these are the four terms, if necessary, we will use them in the explanation of the questions. However, in this case, it works quite well. And so, the W is the need of W, so it is loaded with a... The plus and the minus are loaded. When it is the mass, the need of W is 80. Well, if I continue like that, it will be clear. Okay. Well, it continues like that. So, I think I'm going to have to type this formula. I took it on the Internet, but there were errors. It's someone who got used to typing in Belgrade, but of course there were errors. So I took it on the Internet, and then I told him I was going to go to Belgrade, and if I ask him the question, I'll try to explain it to him.

7:30 So there are a few key terms that appear. So there is the term of mass, and then there is the denominator, which is neutral. We have the mass of the waves, but as you can see, it's not the same as the waves of the world, because there is 1 over 2 CW squared. CW is the cosinus of the length of a wave, which is the length of a weak mixture. So, what do we have as terms in this book? Then, you have the energy, the 5th energy of Higgs. I'm going to continue. So, the 7th energy of Higgs. You have the mass of Higgs. Higgs, in fact, is a double complex. That is, there are 4 fields of Higgs. And there is 5 of Higgs. And the others are not visible, because the same part is exactly the same as in the model of the point H0 and the photon, it is the same as in the previous one, the points are just as far apart, they are charged, and phi0 is not charged. The term is more interesting, you will not have understood, I will not have understood this one, the beta H constant, it is a constant that is there, it is free, it is what we call the Paltrow constant, it is a constant that is there to cancel the beta, the dispersion. I mean, we don't have any of these. It's a constant that has the dimension of a mass. It has the dimension of a mass because, if you look at it, all the betas that are there, the x has the dimension of a mass. So the x is square, so the beta h has the dimension of a mass. Well, then, after, you have the term, that's the term of a constant. Alpha h, and what is it? It's a constant of h. So, in fact, we're talking about hours. And then, here we have terms that are the most common, exactly the same terms that we would use for the longer ones. These are terms that appear in the degree of the square root of the idea of A, the A square. This is the 3D term, it is a public term.

10:00 So, we have terms like this everywhere, then this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this. You can see that the Higgs has started to develop spontaneously, there is a term H4, there are other components that are also H4, and the coefficient that is in front is a coefficient without a notion, what we call the constant of the Higgs wave, if you want to explain what it is, it calculates itself in addition to the H5, which is quite common. We should take notes on that. I think we have done enough to understand the equations. What was the error? The error is in terms of mass, not in terms of motion. In these terms, the cosine of the mass is a square. I'm going to try to calculate it because I can't tell you. There is nothing but one. Otherwise, it would be a mass dimension of 3. In all terms, the energy must have a mass dimension of 4. So, what are the equations? The equations are, we have two angels. There are the unicorns, we started with them. They are responsible for the interaction. We have the two carnivores. Then, as a particle, we have quarks. We have quarks, up and down. The index at the top and the index at the bottom is the index of the generation. That is to say that there are quarks, for example, in the first generation of quarks, we have the quark up and down, okay? In the second generation, we have the squirt, we have the... And then it's just down and up. So that's for quarks. The base of the bars in the quarks is the base of the colors, that is to say that the quarks come in three colors.

12:30 And the fugitive sigma is a collective for the quarks. When we had written the first terms, we talked about the first, there was a term that came up. So the vector, there we have the electron and the neutron in the novel standard, All of these have disappeared because of the mechanism of symmetry. So, in the sense that, for example, you said that the phantoms... I'll show you the third page of the lecture. You will see the phantoms in the third page of the lecture. So, in fact, at the end of the third page, you will see the phantoms. So, all this part, from here to there, it's more or less the same. But in fact, the upper part is extremely important. This is the top part, which will have a meaning when I finish this page. That's how I'm going to do it. So, if you look at the top part, what is there to understand? Well, here it's a truck. So you have, for example, the Duba, the Magda, which is the fuel. The Anis, the Anba, is a generation Anis. That is to say that for the Gaetans, you have, this time, the very good electronic... Thank you for your attention. It depends on whether we are in the video or in the book, but we will see what we are talking about later. It's the same thing. So then, what do we have? We have the bars as parameters. So that was to structure the photons. So the photons are the X plus X point. So the X plus X point are the photons of the two vectors of the point.

15:00 X is the photon photon. We add the photon photon. This is a big break. And finally, the phantom we have here is x0. There are two of them, x0 and x0.3. And after that, it's x. So, before that, we have the mass, the quarks, and then the electron mass. In this model, we don't have a mass. We would have it like this. The mass of the mass of the mass of the mass of the mass of the mass of the mass of Thank you for your attention and see you in the next lecture. Other than that, we have a series of possibilities, which I think are essential, which are the parameters that intervene in the U1s to have the relationship with the mass of the person. Then, we have the matrix of Kobayashi-Maskawa, which is the problem of the constant structure of the soul. The matrix of Kobayashi-Maskawa intervenes in the same transport, but also in another way. This is the answer to the question, the answer to the question, the answer to the question.

17:30 When there is a matrix that wants to pass through it, it is a matrix of trovations, it is not a particle of life, okay? So in the end, all these terms will have a genetic expression, and then we will be able to create a new standard in the future. And the reason why I can present it, in fact, is that one of the things that is essential to understand, and that for the moment we have not yet fully understood, and it is the essential subject of the course today, is the presence of the five elements everywhere. So if you want, what Gamma-5 says is the following thing, what we call Gamma-5, so it's something that is not found in the theory of spinners, is what we call the Kieranite, and by using quantum physics, that the world was not symmetrical, even compared to the symmetry, sorry, and that the Lagrangian of the Sun, he says that this symmetry is Brazilian, and the Earth is not symmetrical. That was discovered by, who discovered it? In fact, Yann Le Pen. So, in fact, what happens is that, what we are going to see is that, to make the calculations, people, to make a calculation with this machine, it is clear that if you try to do the whole renormalization of the product, it will not work, so people use the method of renormalization which is the simplest possible, they use the dimensional regularization, as I said, it is a kind of Feynman, which is far from simple. I don't want to talk too much about that. And they use, therefore, the sub-targeting of Newton. So now there is a problem with the conventional regularization. The problem with the conventional regularization is that there is gamma 5. So what we are going to see is that, in fact, the presence of gamma 5 in Lagrangian... Why is there a problem when we have gamma 5? Gamma 1, Gamma 2, Gamma 3, Gamma 4, Gamma 5, Gamma 6, Gamma 7, Gamma 8, Gamma 9, Gamma 10, Gamma 11, Gamma 12, Gamma 13, Gamma 14, Gamma 14, Gamma 15, Gamma 16, Gamma 17, Gamma 18, Gamma 19, Gamma 20, Gamma 21, Gamma 22, Gamma 23, Gamma 24, Gamma 25, Gamma 26, Gamma 27, Gamma 28, Gamma 29, Gamma 30, Gamma 30, Gamma 31, Gamma 31, Gamma 31, Gamma 32, Gamma 32, Gamma 32, Gamma 31, Gamma 32, Gamma 32, Gamma 31, Gamma 32, Gamma 31, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32, Gamma 32

20:00 In fact, there are graphs that, while the graph of physics has at the classical level a certain symmetry, what we call the spectral symmetry, it is impossible to re-normalize the graph so that this symmetry is still valid in the world. And the reason is that there is an ambiguity in the definition of the term and that we have a problem. To define counterfeits that are invariant in the same system. So, the group of symmetries that appear is, we will see, it will be the unitary group of the algebra that I told you about last year. We know that the cohomology of the algebra of this type of algebra is calculated by a coefficient. So, it is absolutely not surprising that we find a link with the cohomology of this type of algebra. It's been a long time since I had a lecture on mathematical physics, but it has taken an absolutely considerable time. To arrive at the formulation of a precise mathematical result, which is not a mathematical one, but which relates the actual physical calculation with the mathematical one. That's what I'm going to explain to you. And so the theorem with which it is going to be linked is the theorem of the local analysis in mathematical physics. I'm going to explain this theorem to you, not in relation to the standard method, it's finite. In terms of complexity, it's the same. So, what is a theorem? First, what is the frame of a theorem? So, the frame of a theorem is exactly the frame that will allow us to understand geometrically our instruments.

22:30 So, I'm not going to... What is new, what is new in the standard language compared to... with the standard language, etc. At the beginning, there is something really new. And what is really new is the evolution of symbols. Of terms. So, there is an extremely simple way to explain the evolution of symbols. The idea of a spinner is that you take a passive space and you take a fiber and you call it the spinner's fiber. You have your passive space and you have on this passive space the spinner's fiber. In fact, in quantum physics, it's much simpler. Because the spinner's fiber is now everything. That is, it's the space of Hilbert. It's not a fiber above your space, it's simply the space of Hilbert and Kahneman. And our space X is no longer represented as a whole, but as an algebra of coordinates that act in space. So you have to think of H as a very large sphere. So now, when we look at the speeders, we have the uniformity that acts in the speeders. This is now replaced by the angular element of its inverse and we will define it. So this is the operator of Dirac's partial algebra. So, the framework in which we work and the framework in which we study mathematics is what we call a full spectrum. They are obtained based on the interest of the operator, which is very similar to the operator of Breck, and which constitutes a kind of function when we look at operators, which are operators that are manufactured from the gene.

25:00 So A1 is going to coordinate, A2 is going to coordinate, and A3 is going to coordinate. From the D operator, A3 is going to coordinate, A4 is going to coordinate, A5 is going to coordinate, A6 is going to coordinate. These operators, we will be able to measure them, measure the recipe. To measure the recipe, what we will do is to see the trace of P times the power of D. We can look at the physical part of the equation like this, and they all have the same value. So that means that if I take a trace of P times the negative power of P, this will be traceable, and this function will be a function of the value of S, which will be a function of the value of S in the unit. As soon as S is the value of S0, the function will be different. So, it's a puzzle, isn't it? A puzzle, yes. It's a puzzle, it's a puzzle. We make our puzzle in the world, okay? And it appears in singularity. And this set of singularities forms a spectrum, what we call the spectrum of dimensions, that is, the dimension of the space in which we live. It's a set, it's not a number. And it's a set that is based on the superior dimension, that is to say, the physical dimension of space. And space is written in the lower dimension. So, the first part, that is to say, We define the residue, in this case, the residue of the equation of zero. It is done in this manner, it is defined as a trace. In reality, it is a simple hypothesis. It is defined as a trace of the equation encountered by this phenomenon. What we are going to do, in addition, is to calculate it. It is not to be a little bit senseless. The theorem, which Kahneman has demonstrated to Kahneman and Kahneman himself, he says that we have a specific hypothesis, 15 minutes, which is calculated. If there are comparisons...

27:30 So, if you want to know what is cohomology, it is the analogy of the logic of Ram in the case of a random object. What is cosinicity? It has a component. And then, the remarkable fact that I had already mentioned is that the combinatorial factors that appear in the component of cosinicity, which in itself is quite simple, the combinatorial factors that appear are the same as the factors that appear in the universal framework. You can tell me, there is a chance to fail, but 1 is actually a shift, I wrote here 4 plus 1, you see. In fact, earlier I had 4, 4 plus k2, 4 plus k1, there it is because we shifted, it is sometimes the opposite. So we have a co-cycle, well, in a certain cohomology, we do not need to know anything about this co-cycle. So this cohomology, if you want, it is in what we call the bi-complex, small b, large b. That is to say, these are multilinear forms on the jet that verify certain rules. And these rules make us have a complex view. When we calculate the total view of the complex, we obtain the following. So these are the rules that we have arrived at. I can remind you of these rules. These are the following rules. B is the operator of Rothschild. So, for example, b is a multilinear form evaluated with a diffuse variable, a0, a1, b1. This is simply the internal sum of a minus 1 to the power of phi, and then we will put a0, etc., and then we will put aj, aj plus 1. We will contract like this, and then there will be one last term. Here, if I wrote the last term, it would be minus 1 to the power of n with an, an plus 1. There is another term with minus 1 to the power of n plus 1. This time, it is really cyclical, if you will, that is to say, we come back to zero. We take an plus 1 to zero, and then an, and we do not change the others. There is another edge, which is the big B edge. So the big B edge is written as big B equals the cyclic antisymmetrization of the B0 edge. And B0 is very simple. B0 phi evaluated in A0, now with one variable less, because B0 goes in the other direction. It is simply phi evaluated in 1, A0, etc., A and B0.

30:00 So these are very, very general operators, completely simple, which exist for all of Japan. And Vitalgule, if you want, which replaces Ramp's homology. So, if you want, this theorem, the theorem we talked about, it's a theorem that calculates the classes of contraindications of space in the universe. That is to say that this space, it is given with its operator Dirac. This operator of Dirac, there is at least one, at least one vector or two. Yes, you're right, but I suppose it's normalized. In fact, I would only look at normalized squares. So I want to simplify as much as possible. All of which may be a little too rigorous, at least not in my opinion, because here we are talking about two liters. So what is the observation that we have made recently about this theory and about physics? So the observation that we have made is the following. All these subjects have the same problem as Gamma-5 and also have the same problem as the home developers who have understood how to treat Gamma-5 with real data. They have written a recipe, a recipe that is perfectly real. What we are convinced of is that in fact this recipe is identical to a recipe that I have written in my practice. It consists of taking the ordinary space, with its triple spectral, since we create the Euclidean, take this ordinary space and make its product by a space that we have found, which will have the dimensions of Z, and which will be a complete space. It will be a pure dimension, that is to say, it will not be that the dimensions will be like the point of the non-complex Z. So in fact, to be honest, this space exists in its ordinary sense only when Z is a real positive number. And we will have to make a strong imagination effort. To see what it will be when z is equal to x. And you have to imagine that there will be a fabulous monochromy,

32:30 that is to say that this space will not exist for a single value of z, it will depend on the monochromy. That we don't understand. And this monochromy must correspond exactly to the image of the monochromy that I gave last time, that is to say, this monochromy with decimals and so on. That's why we have to concentrate on making correct and precise calculations for z, real and positive. And you can understand that when we do the magnetic approach, it makes no sense. But I would like to say that this is the space in question. I don't need it, exactly. For counterfeiting, I don't need it, I need the real ones. However, to understand vulnerability and to understand the geometric image, we will need counterfeiting. So instead of defining these spaces... When you immerse yourself in space, you see that what is very pleasant to see is that the product of space that we use in our work, it is a great luxury to talk about non-physiological space for climate space, it will no longer be when we make our product through dimensional space, because there we will have a space that we spend all the time on the universe. And well, it's a classic recipe of the theory of the character of Dirac. What is this cohomology? Well, it's simply that the operator is tensioned by 1 in the first space, plus gamma 5. Look, we can put gamma 5, but it won't move down this one, in the first space, tensioned by 1. What is the point of putting gamma 5 here? The point is that gamma 5 is not connected. You see, when you go to do the square of the square of the second, there will be no square of 3, but only 2. So that's the point of having gamma 5. So, now we have to be a little free, we have to do the physics, what we are going to look for is, for the dimension of the wave, we are going to look for an operator d z which is exactly the result of what we want, we will see that's what we are going to do. We want the trace of the exponential of lambda d z squared to be exactly given by pi power of 2 over lambda power of 2 over 2. That's it. That's the answer. And once we have this answer, I'm going to say that all the things we do are in the same category.

35:00 Unless it's the answer. So that's what we're going to do. So there are some technical problems. I don't know if you can understand them. But we have to solve them. I'm going to tell you what this space is. As I said, we'll have to get rid of the freedom. The freedom of expression, the freedom of notation. It's actually... To do things, for things to be ideally simple, it is better to take a space of type 2. So what is a type 2 space? A space of type 2 is a space where, instead of saying that the operator D inverse is a compact, we are not talking about the ordinary sense, what you have is that D inverse belongs to the compact in a type 2 factor. So the theory of spectral tripes has been extended by Thierry Farc, Jean-Philippe, Alain Carré, Jean Louis, I mean, in the case of type 2. We could do it with a little bit, but we would have to practice a lot more. Basically, it means that when we look at the commutant of the energy generated by A and D, the commutant of the energy generated by A and D is the liquid, and the representation generated by A and D is the liquid. This is what happens when we exclude. And now we are going to assume that the commutant of the energy generated by A and D is a factor of the liquid. This is a technical debate because we would have been able to do it, and we would have been able to do exactly what I am saying. We would not have obtained this equality in the form of two clauses, that is to say, we would have obtained the exact equality, but we would have obtained the equality in an exponentially abstract way. So this is the definition of operator B. Okay? An operator whose spectrum is less than 1 is less than 1, and its spectral measure, it can be, it's a measure of 1. A factor of 1.

37:30 And it's a factor of 1. That is, if you want a measure as a measure of 1, you can't have a spectral measure compared to 1. So, that's why it's so easy. So, where is the fact that your operator of z is a power 1 over z? That's very interesting. I don't know why, I didn't say that yet. Why is it a power 1 over z? Z is the operator that has four spectra. The operator in Z has four spectral measures. That's the measurement. Well, you have the choice. That's all I ask. I ask that the operator Z has this probability and that it is also symmetrical. I mean that the spectra is negative and so on. So, why do we have to take an extension on Z? That's a thing... Well, if you want, what happens is the following reason. It is that in quantum geometry, the infinitesimals are calibrations. That is to say, there is a unique notion of an infinitesimal in order 1. An infinitesimal in order 1 is an operator in the proper values of the three conditional ones. Okay? So, if you want to be able to talk about the integral of dx to the power of z, whether it is integral or not, you have to take the power of 1 over z of something that is integral to 1. That's what I'm saying. So the element of length in our space of 1 over z is the operator of 1 over z to the power of 1. It's the inverse. That's it. Thank you. Well, after that, we have to normalize a little bit. There is a normalization factor. We talked about it earlier. The normalization factor is the variable function. So, you have to verify that this is a sense. Because the human being is capable of it. And that it is a development. It starts with the development. It's easy to say. So, now, if you calculate this, you calculate that the answer is exactly the same. It's not true. Thank you for watching this video, see you in the next one.

40:00 So, we do the calculation and we realize that the spectrum of the dimension is simple, that is, there is no simple, and it has only one point, it is the point Z, that is to say that it is a space that is purely of dimension Z, if we speak in terms of motifs, it is not a fixed motif, it is a pure motif of dimension Z, a pure motif of dimension Z. So, when we do the equation with a curve, we calculate the integral and we find the function of the function of the function of the function of the function of the function of the function of the function of the In this way, no matter how you look at it, we can see how the project between 2014 and 2013 ended up with this error. So, error is a function that has to be taken into account. In this way, this error in the function of z is exponentially higher. That is to say, when z tends to zero, it decreases faster than any polygons except z. Okay? And then, attention, this is sectoral. That is to say that right now, we are like in the theory of Ramis and Descartes, etc., we are in the secular space, and it is because of that that there will be ramifications. So, if you want, this is the perfect moment to start to realize that we will not turn around the origin, because if we turn around the origin, obviously, the exponential of minus 2 over z, if z is negative, it grows extremely. So, it is from this moment that the problem of the correct definition of what is happening around z arises.

42:30 What is the meaning of the 2 there? The 2 which was the power? Why is there a 2? It's because, remember that it was exponential of minus t squared. Square of the earth. So the earth has a power of 1 over 10, so it has a power of 2 over 10. Equal to 2 over 10, which is equal to lambda. So we have a problem. We have two things to do. We have two things to do if we want to stay on earth. And we will have to understand the rest. So we will see that the key for mathematical mathematics is the fact that when we have a geological geometry, we automatically have gauge potentials. And these gauge potentials actually correspond to the fact that the most independent geological geometry has internal fluctuations due to internal automorphisms. And these internal automorphisms do not exist in reality. So I'm going to explain the mechanism in the case of non-computative in general, and it's a mechanism that comes from the equivalence of Morbita. The equivalence of Morbita in the case of commutative is in what sense? I mean, it has an electric essence. That is to say that two agents of commutative are equivalent to Morbita if they are advanced, they are identical. In the case of non-computative, it's very simple. And so, the notion of quantum physics, of this notion of the deformation of mathematics, in the old age of mathematics, has automatically changed over time. That is to say, how did it come about? You start with mathematics, so you say A, and you say I don't know. Well, I don't know is given by a spectrometer. So, it is given, if you will, by an action of mathematics in the universe, which is an operator. I'm going to send it to you, I'm going to send it to you. So now, to understand mathematics, you have to study it. There are also anthropomorphisms on A, anthropomorphisms on A, anthropomorphisms on A, anthropomorphisms on A, anthropomorphisms on A, anthropomorphisms on A,

45:00 Not in Hilbert space, they are contractually contracted on the object. Now, the problem you have is how to define operator. It's a problem because, a priori, it says nothing. I want to define my operator by taking, for example, the equation that the operator describes. Apply a tensor here because I did not start. Well, I would like it to be here, tensioned by delta. Because after all, I have the operator delta. You see, it's going to work. That is to say that if I have A here in this state, I know that it is equivalent to A here in A and A, and from this point it will not work. It will not work because A and B do not match. So you see that the other solution to make it work is the commutator between B and A. So while I was thinking about it, I realized that the same solution is completely random. And it is given by what? It is given by the following equation. It is given by the operator d'equal d'. In this case, we have a connection between the two states, and we have a value exactly in a connection. So, what is a connection? In this case, it is extremely simple. It is a vector connection. The connection is given by a linear application of the projective module of Puccini, epsilon. In short, the two modules are connected to each other, and they are connected to each other by a certain bimodule, which is called the bimodule of an angle. At the moment, the bimodule of an angle is called the bimodule of an angle. You can see that the bimodule of an angle is called the bimodule of an angle. You can see that the bimodule of an angle is called the bimodule of an angle. and an extension of the operator of the spectrometer on the moon. So, this is a phenomenon that does not exist in the cognitive field,

47:30 which is that the cognitive language is always good. The cognitive language has always the same equivalence. When it has the same equivalence, it means that this auto-cognitive equivalence will create metrics that are equivalent to the metrics that we have. And what are these metrics? They are not given by the history of the potential of change. The potential of change is completely calculated by the theory. So you see, in geometrical mathematics, there is the potential of internal, trivial changes which are automatically generated by the geometry itself. And going further, I mean, well, I don't have time to talk about the real structure, about the energy, but going further, if you will, what we perceive is perhaps the structure of the geometry. There is a structure in two stages. There is an internal part of the geometry and there is an external part of the geometry. And this is the example of the fact that for the automorphisms, which play the role of symmetries in validation, there are internal automorphisms and external automorphisms. When you take an automotive geometry, it has a rather rich structure of internal automorphisms. So we will see it again, the avant-garde of Alexander, where the needs of people are exactly the same. And when we have written the correct things, we will also have the application, we will also have the emergence of Einstein, Einstein-Wilhelm, who will appear with Plage-Milvain in the future. So, if you will, it is something that is extremely simple, these things, at the conceptual level, it means that when we do non-competitive geometry, even if there is a little bit of non-competitive, So now we are going to see a small variation of this, and this small variation will give us exactly what is called in physics the evanescent potentials, which play an essential role in the theory of all the

50:00 The question is, what will happen is that these rules that we have given, we can interpret them in general, and we will see that it will give exactly what physicists call an analysis potential. So, how does it happen? What we do is, we will now be interested in the symmetries that we call the chiral symmetries. If we are interested in the chiral symmetries, we will not be interested in them. Automatic. If you have an agenda Z on two gradients, instead of taking a commutator, we take a graduated commutator, etc. That's what we're talking about. So now, what we're going to be interested in, we're going to replace our agenda with an active agenda, which is the agenda that would be replaced by the algebra and the Z on two gradients. We're going to see that if we didn't do the conventional regularization, that is, if we went purely in critical dimension, it wouldn't change anything, it wouldn't change anything at all. If we do the organizational organization, it will be a change and we will see that it is a change. So, we are going to look at the gene. It is simply two copies of the gene A. It is crucial because if you take gamma, it is an element that commutes with elements of A, the gene A. So, it is square and straight. So, it is square and straight. It is crucial to see that it is outside. It takes more than one in the zone. But now, we are going to look at this graph, we are going to see the Z on the graph and we are going to show you the graph. We are going to take as a gradation the gradation which is the identity on the gene at the start and which is minus 1 on the graph. On the right, we have the square of Gana. We do this. And now, we do the product of spaces with the space model. When we do the product of spaces, the operator of Dirac for the product space is the operator which is the sum of two operators, bars and hats. The operator of the bars is simply D, transformed into A. And the operator of the hats is Gana, transformed into A. This is the product.

52:30 So the operator of the seconds is the sum of the two. Now let's look at the general set. What do we have here? Well, the operator gamma is anticommitted with z. So if you hadn't changed the operator of the seconds, there would be nothing. There would be no new potential, since it is anticommitted exactly. It would not have created a new general potential. So that means that if it is without problems, it is not with bars, because gamma is anticommitted with bars. So the operator gamma is non-negative. But on the other hand, it is not anticommitted with z. Why? Because gamma commits with gamma, so it does not anticommit with gamma. So when you use the combinator, what do you get? You get new potentials of the gauge, which are bizarroids. They are, if you look at the scale in front of you, they are the form of gamma A times H. So now you open the chronicle to look at the chronicle, what is called the resistance potential, which you will see next. That is to say, it is the potential of the gauge. All of these terms exist only when the dimension is not equal to the physical dimension, that is to say that this thing, that's why it's called mathematics, we'll see maybe in time that there will come a time when what we call geometric algebra will exist, and so, you see, it's very interesting. So, what is the explanation in the sense of physics? I mean, what is the explanation in the sense of the general function of the system? You see, what we did by changing the algebra, that is to say, by taking as an algebra the elements of the form a plus b gamma, we added new symmetries, which are precisely the chiral symmetries, because they invoke gamma. And so, what happens now at the level of the algebraic algebra and at the level of the functional algebra? I don't know. First, we looked at the thermodynamic functional algebra. That's why there is an excellent source, it's the book of Goldman that I just wanted to see. So, what happens is that we do the integration of everything. And it's important, when we do the integration of the equations, please, it's the fact that, precisely, we do it as if we started from the beginning, that is to say, when we integrate, we integrate with the exponential integral of the equation of the equation,

55:00 And this is what we are doing here with two states of xixi, two states of xixi. And two states of xixi are different from each other. They have very similar mathematical integrations. So you can see that they are very similar. It is well explained by the code. And so now we have the transformation of the gauge. And we are looking for the transformation of the gauge. For example, chiral. And there is one thing that is very obvious. If we look at the line, we realize that the transformation of the gauge on the xixi is the transformation of the ordinary. But the transformation of people in the same state is gratuitous. We will use the equation to calculate how the intergalactic wave varies as usual through the transformation of people in the same state. There is a negative force, there is an evanescent force. So now, if you want, we have exactly the same results. To ask themselves the problem of anomalies and to do the calculations. But what we will see, so that's what I'm trying to do, is that at least in the lower dimension, because I haven't been able to do the calculations, but at least in the lower dimension, we will find exactly the same terms as in the theorem of the with the calculations, in the right dimension. So that's really what's surprising. So now we're going to have a formalism. And you see, it's a formalism in addition that will apply to any space of communism. Because you can go to any space in the universe, you can make your product by the history of its dimensions, so you can apply it to the universe. And even in HGV geometry, I mean, it would be necessary to get the frame of the motifs to be compatible with the frame of the geometry of the motifs. I mean, it's one of the first face-to-face that happens. There, there is the theory of motifs, I don't know how to explain it, we will see, we will have an additional image, and there is the geometry of the motifs. So it's normal that at some point or another, they are face to face.

57:30 So here, they are face to face in relation to this program. And we'll see that they are also, in relation to the theory, in relation to the grammar. But in any case, we have a good framework and we have a reasonable definition of the five dimensions of algebra. And here, we always respect the knowledge of reality. U is a unitary, and that's why ASCII... Absolutely, no, no, no, no. A is an erudite element. A is an erudite element of the HLU. Jacques, you're right. A, here, verifies that A is equal to 3. I'm not going to talk about the real structure. It's not a computation, but we'll see how it works. Well, now we're going to start the calculation. And then there's something else, I don't want to dwell on it. So we are going to write Feynman diagrams. And these Feynman diagrams will already have a specific meaning. I will not do all the work, I will do the calculation of the number of numbers in the calculator. It would be difficult. So we are going to start with the theta, with the square root. In this analysis with Henry, there was the zero-order component, and the zero-order component was not a residual, it was a regularized trace, i.e. it was a limit of the function of the mass with a zero-order, i.e. a limit of the supertrace of A to the power of zero. We have shown that its value is finite and that it is given by the term minus zero in the mathematical part. So, how do we do that? You will see that it is the typical calculation that we will do later. We will do the calculation later, but it is not an example. So, how do we calculate? First, what is the meaning, in mathematical chemistry, of a graph like this?

1:00:00 You see, when you take a graph, it is like this, for example, in which all the lines are unique fermions. It's quite simple because we have a fermion propagator since we have the T-Rac operator and we have the length element. We know that it is the length element that is the fermion propagator, so it's B and A. And what is the fact that we took the graph? Well, it's in the trace. What is the result when we have the external potential which is E? Well, it means that we took exactly the trace of E. We have B seconds. Why do I say B seconds but not D? Because I'm doing Imaek. In Imaek, I have the operator B seconds. So, let's do a calculation. We will see that this calculation is very simple, but it will be very representative of the understanding of the equation. So, what do we do? We will have to do a good physics. We will have to say that the inverse of the second is the second times the second minus two. The second is the bar plus the hat. So it's the bar plus the hat times the second minus two. What is the square of the second? We will not be able to do it with a three-dimensional map because there is an anticombination. For the second square, it's equal to d squared squared times d squared squared. Okay? There are no terms for that. We only learned the sugar formula. The second minus 2 is the integral of the final value. The exponential minus t, the sum of the two terms, goes away, but the commutant goes away. So I can't calculate the exponential. So it makes the exponential minus t d squared squared times the exponential minus t d squared squared. Well, what is my potential E? I remember my potential E, it's gamma A of the hat. So the word the trace of E to the inverse second is the word the trace of gamma A of the hat times d bar plus the hat for the second of E. Okay? So we wrote what we need up there, that's it. So wait, why don't I have the term of the hat of the bars? Why don't I have the term of the hat of the bars? I had chosen the name of the character hat so that its spectrum is symmetrical.

1:02:30 The trace of an operator that is symmetrical in its spectrum is zero. So, the powers of an impeller in an impeller are zero. So, you have only the powers of an impeller in an impeller. So, you have a trace of a, gamma a, of an square impeller. This is the second factor. Three seconds minus two. In fact, that's what it's worth. That's the formula I'm going to give you. That's what it's worth. It's equivalent to the formula of the trace of gamma a, square impeller, exponential minus t of the square bars, exponential minus t of the square impeller. But now, this trace, it is factoristic. Because the operator of the chessboard lives in the space of z, and the operator of the bars lives in the space of the bars. So the trace is not correct. The terms that belong to the bars are gamma, a, and the exponential quantity of the square bars. I'm going to break the bars now, because I don't know what's going on with the bars. And we have the trace of what happens in the complex, what is it? It's the square chess that gives me the z squared, and the exponential quantity of the square chess that gives me the exponential quantity of the z squared. What about this trace? Well, this trace is obtained by deriving the universal formula from earlier. I remind you that we saw that the trace of the differential equation of z squared was b over t by epsilon z over t. When we derives precisely at the point of z over t, we obtain on the left the trace of the differential equation of z squared, and on the right we obtain the derivative of the function of b over t by epsilon z over t. Thank you for your attention. The gamma gives us a factor of minus 1 and the limit when we go from 0 to 0 is 0. So you see, it's typical of the kind of calculation that we do in the computer after. But what it tells you, it tells you that formalism is very consistent. That is to say that we can calculate the formula, we have to calculate this number.

1:05:00 3, 2, 5... And this graph, as simple as it may be, is a very trivial information because, for example, in dimension 4, the component phi0 is the class of contraindicated P1, as you calculated it, it is exactly the class of P1. So, in fact, the state of supernova is in the form of P1. So, the program, if you will, is the following now. We have seen the component of phi0. So, the program is to calculate the equivalence, for example, which is more complicated. Let's move on to the conclusion of the inter-algebraic algebraic argument. And what is the idea? The idea is that what characterizes the standard model is probably the minimal solution to the elimination of the elements. So it is essential, if we understand the idea, to have a good entry in the geometry of mathematics. And really the anomalies as the physicists defend, because it's easy to say we're going to do things that are related to anomalies. We've heard for years and years that anomalies are related to Atiyah's theorem. That's very nice. What we want is an explicit calculation with graphs that give the same result, exactly the same result, as for the standard model. And in the standard model, we saw earlier in the formula, As we said earlier, there are forms of equations here, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there, there,

1:07:30 The charge of the power of the atom is minus one third. That's why the proton which is UDD is neutral and the proton which is UUD is of charge of one third, minus one third. So, in fact, it's not the charges that are the difficulties, it's the supercharges. Because charges end up combining the actions of U1 with the actions of S or E, or S or E-. So the most important number in the equation is a number that appears in scores. A 4 here for the electron, which in fact is a 2, which is the hypercharge of the electron which is a 2. The hypercharge of the quark up is equal to 2 thirds. The hypercharge of the quark down is equal to 24 thirds. When we return to the annulation of the anomaly, in fact, what will count is that the sum of the cubes of these numbers are equal to 1, which is incredible. If we had a linear relationship between these numbers, we would agree. But what we will see is that the anorex of the triangle, the fact that it is 1, is the effect of the sum of the cubes. And that's what led to the show of Diocleus and Magnani to predict the descent of the quantum. That is to say that without the cork, the model would not exist in the sense that it would have an anomaly, which means that we would not be able to normalize in a invariant way compared to the symmetry. So there is a kind of cataract phenomenon. If we tried to make a more simple model of the response, which would be, for example, electrodynamics, we would perceive that we would have an anomaly. So, in fact, if you want, one thing that has motivated me the most in the research of the last few years, and that is in particular the work of the professor of mathematics on the spheres of the universe, is to understand in what sense the standard model is the smallest solution. Well, it does not seem small to you, but we will see in fact. That is to say, in fact, we will see that the standard model is a...

1:10:00 Any small correction in the geometry of space-time will be explicitly explained, in a completely general way. And then, there will be a completely general reception to do the calculations and to give. But there remains an absolute mystery, and that's why we all do this work on this subject. This mystery is to see in what sense this modification of space-time is necessary, Why do we believe in things? Because things work, but they don't work in the same way. And in what sense would there be an anomaly if we were to talk about QED? There is something to say about the complexity of this subject. In fact, when people do QED, there is a quantum physics project. The quantum physics project is a quarter of the first year. That is, it is the first line without the square of the fields, it is two terms, it is this term there and this term there in the middle. And still without the inputs and so on. So if you want a standard model, you have to implement it. There are a lot of mechanisms, there are a lot of mechanisms to do it. When there is a problem, you have to solve it. But in what way, precisely, it solves the problem that QED does not solve. What is funny is that... What's really funny is that when people at the beginning had QED like that, what was striking was the simplicity of it. And what was complicated was to do the calculation up to five loops, or four loops. And that's why people were able to calculate the moment in the middle of the metro and do calculations. But as soon as we changed it like that, and that, Witten says it perfectly, even calculating in one loop can only be done on computers. Why? Because there are so many terms in one loop. That doing it by hand is like if I wanted to write on the board the Lagrangian of Newton. It's impossible. It's practically impossible.

1:12:30 So there is a radical change of philosophy. And then, you see, it is indeed extremely... What is brilliant, at the philosophical level, it is there that I prefer to have... What is very brilliant at the philosophical level is that we would understand if we had the Q&A Lagrangian. That people would say, we understood what space was, space-time, namely the space of Newton. Maxwell's equation, or Dirac's, gave us the Lagrangian, and that was the end of the story. Here we would say, very well, we live in the space of Nikoski. And what do people do afterwards? They say, well, we live in the space of Nikoski, but the Lagrangian is more complicated. Isn't it weird to say, we live in the space of Nikoski, but every time we have a new term in the Lagrangian, we add a new particle in the space of Nikoski? We will see that we will completely reverse things and we will say, no, this is the project that has been tested millions of times at CERN, and that is what gave us. But now what we have to do is to say that the logic is extremely simple in terms of the new algebra. The calculations will be very complicated for us, but the conceptual idea must be the truth. It must be extremely simple. That's what I'm going to say. But what we will see... That's why I made the Ymbrègue and all that. We are very far from it. What will be extremely interesting is that the way in which the geometry is regulated in the Ymbrègue, which is a product by this X-Z space, is exactly the same way as the one that will allow to write on the Langell in 2D. That is to say, it is to make the product of the ordinary space by a new space. In the case of the Ymbrègue and the X-Z space, to catch the standard model, it will be a finished space. So, in both cases, the operation is the same. So, obviously, it suggests that we have to go through the operations together and that we have to make corrections to our naive vision of space-time. These corrections are of two kinds. On the one hand, the slightly non-complicative side, which will improve all the terms of the standard equation,

1:15:00 but secondly, the same rules. Secondly, what we need to understand is that instead of being on the classical section in the fibrous that we explained earlier, and instead of moving straight to the classical section, we have to follow the ramification and we have to place ourselves in that space. And so it will give us two corrections of the geometry. We need to understand how to matrix them. We are going to put together these two corrections. That's what I'm talking about. Why? Because what is done at the level of the Lagrangian is the classical Lagrangian. The Imregg is the normalization of the angle of the Lagrangian with a quantum function. But you have to manage to put everything together. But in any case, I hope you see it gradually appear in your perspective, a mental image of space-time that is much more subtle than the space-time that comes. That is, on the one hand, there is a normalization of the path through Imregg. And on the other side, there is an Erzard without any relativity, and it is the two that must combine. That's what I'm going to try to do. Obviously, things have to work. And the first thing we're going to do is to do much more sophisticated calculations of anomalies, etc. to see, for example, the case with the theorem of Newton.