MHV Rules in gauge theories

0:00 And then, of course, one has to examine all the boxes. So, I guess, now that we've produced the forecast of each box function, now we want to see how the forecast actually turns into the real box. We focus only on one box function, and then what we can do now is apply some of them to each of them. So the next thing is that for each channel, fv, vv, v square z, and q square z, we will rewrite vv over z in terms of a dispersive measure of that channel. So the next channel will be vf, fv over fv minus x. And then, by connecting the four cuts which belong to the same box functions, we get this function that we just currently had, which I will describe. The phase space interrupts compute the discontinuity in the channel, so it is immediate to see that these four numerals here are compared with the only discontinuities of the box function in the core channel. And then, for each discontinuity, we perform a recursion interrupt. Now the question is, if the box function f equals to f, if we compute this, then we have proven that... By using chemistry diagrams, we do reproduce the spectrograms with an angle of 4. So, one thing you can say, really, is that, obviously, we start from this point in the curly R as the J discontinuity of the Boltzmann diagram. But then, one might argue that the obscure structure of terms can be introduced by this procedure, and also, as I said, there are infrared divergences in this calculation, so this argument is a little bit forward. And third, I think it's quite easy not to do that, so I'm going to go back and see what I want to say. This is what we say. This is our final result of the discovery of the members of four. So this is expressed, again, three antidotes. Some of them, two of these, are a bunch of coordinates.

2:30 And the coordinates express... As a term which contains all the different divergences, it is the same as the term which appears in the use of box functions, scalar box functions, and then there is a finite path, the finite path of movement. Now, the funny thing is that the term which came across is not actually the same, which is known in the literature, so it might be either wrong or... So, here I wrote in black the homo-expressions, the expectorations, which is even written in the literature, but in effect contains something like five dialogues and one logarithm, whereas the expression that we found here contains only four dialogues, so it's a little bit shorter. And then, okay, they agree. So here there are four dialogues, here there are five, so we need an identity which has nine dialogues. In one case, we could solve this problem. In this kind of case, there is only one identity component, which has nine galops, and then there is another identity. But then it would be tricky to find the correct assignment for this variable, x, y, w. It doesn't take long. We have to respect this requirement, and we have the correct assignment. It turns out that this string forms the final part of the heliport span for our training case. And if you want to play with the logs, you can find different elements in the different cases where you have only five-part post-capturing and four-part scathing and then you've got post-capturing amplitudes. And again, as in the three-level calculations of Cacciato, Sergi and Witten, each of these NH3 diagrams are two-leveled with a large number of conventional final diagrams. And also we found Mr. Slagy's still-born expression for the two-mass even-boxed function which we gave earlier for their laws. And as I said, the results of this game is presented within a set of burglars of that might also have, in all of which they are more about the constructively approached so-called deriving attributes.

5:00 One brief comment on the piece of space interpretation of this one-loop scattering ambulance. So, in terms of Witten in his paper, which I think is the last one, he studied localization properties in this space of the 100 scattering amplitudes. So, Witten, in his first paper, proposed to produce a couple of either elements in this kind of localization properties. Of course, nobody wants to go through this half-trivial force, but in a more efficient way, in a coherent space or momentum way, by using some... In particular differential operators. So one applies the differential operators to the other and by doing this one can learn whether some modes are collinear or whether some modes are coplanar. So the results of the analyses of Katsaris and Witten show that there are basically three different kinds of twistor-shaped diagrams which appear in the one-loop algorithm. So there are two lines that correspond to 2-MHV catalympics, joined by a piece of propagators, but then there's also a third diagram, a third physics-based diagram, where one of the two ones wanders off. So now, this third diagram is more complicated to reconcile with the two calculations that we have seen, because the other one has only 2-MHV diagrams. But then it turns out that, you know... The third diagram is naturally due to the presence of a new disturbing application of the differential pericluster, which was called the holomorphic anomaly, which turned out to be a very powerful new way to compute loop diagrams by actually computing only trees. The remaining fields that we will show briefly are generalizations and properties.

7:30 I'll see them. Now that we see that we can reproduce a scattering amplitude in n-1-4 so we can mirror that, let's try to go down to the symmetry, for example, and try to calculate objects in n-1-4. Now, of course, I didn't practice this for you. Scattering amplitudes which have not maximally traded invariably, so next to the energy amplitudes. Okay, this was done in a paper and also by two other models. We can start in a paper which is here on the page, and then we'll follow. So, okay, the first thing to observe is that to simplify the calculation, one can perform a specific semantic decomposition. So we just write the integral 1 vector 1 to the contribution of amplitudes and scattering amplitudes The n-quad-probe constitution that we have already concluded finds three times the constitution of a chiral multiplex. This has also been concluded by Ernst-Wilson, Lange, and Kossow in 1904, so we have again another expression to check again. And the result, I'm sure some of you should have heard the result, again the triumphant impact was out, and now this point in English, and a few calculations here. All of these contain only the sterile box functions, now it contains also triangle functions, and also another feature of the results is that the time is extremely dependent on the locations of the negative entities we want, time and rate. The time of mathematics is almost exactly the same as before, and we need only to compute the space where the two negative entities sit on different vertices. And so on and on and on and on and on and on and on and on and on and on and on and on

10:00 There are also bubbles that can be incorporated as special cases of the primals, when one of the two massive legs of the primal degenerates to a massive leg. This leg is a massive, but this is a bunch of legs. You can see that in this triangle chart here, the triangle part that appears in the field of priority is given by this fraction, and in our approach, again, it is reconstructed from the cup. Before we had the scalar box fraction, we were summing over four dispersion literals, and each literal was for one of the four cups, and here we have two cups, this cup and this cup, and we reconstruct it by... There are just some in the programming class. And also train the eta in the algebra. One last slide. So after an hour and a half, I will now confident that it is possible to apply this method also at a different level. And then one can at least obtain, assuming that one can obtain all the cat-constructible attributes. So all the attributes which contain cats can be obtained by this mean. So why don't we start, so now we want to do something new, so we focused on the mathematicians and physicists evaluating attributes that are not including pure geometry. And the attributes, however, they contain rational terms and also cat-constructible facts. What turns out is that by this method, we compute only the mathematical part, so only the mathematical part of the term is going to appear. Also here, there are two X-men in the composition, so now we have only two ones, because we have three of them in, but we can rewrite this contribution as a contribution of n equal to 1 minus 4 times n equal to 1, and the remaining terms we compute with a scalar contribution.

12:30 And some theories are very tough, just small complications, so it's not very good to try to explain it. But again, it's expressed in terms of the finite part of the state of box functions, and in terms of private functions, where the ones which appear in the previous calculation are equal to one, and together they are equal to one. And another theory is that the coefficients of the finite part of the box functions And of course one wants to check with the non-regard and from the past, so in the past one, so Bernis and Krauseberg were able to compute their own five-to-one scattering amplitudes, including their actual parts. And so we, our general formula is what you see here is thin, and also, we have some numbers also that tell you that we have to check new approaches from time to time. The case where we can use more work, we have to further check what we're doing correctly. And so in our results, it's a new... This is a prediction for the case of magnetic influence and antimagnetism. Finally, there are many things to do. Many of them are listed on this stuff, so it's possible that one of these two people would like to find a similar formula to compute the whole algorithm in non-specific theory. Thank you.