Hi guys,
one question in this growing amplitude business that i don't understand. Usually one says that conformal field theories do not have any non-trivial scattering amplitudes because one cannot define asymptotic states. But say we consider now N=4 Super Yang Mills and moreover treelevel...
Ah, thanks for the explanation. One more question about this:
So coming back to the numerator, i could rewrite is in terms of a four-vector product as:
\langle a |L|b]^2 = (2q\cdot L )^2
where q is a four-vector build from the spinors \langle a| and |b].
Under the integral sign i could...
Hi and thanks for your reply. Look for instance at hep-th/0612007. They never do the integrals (they reduce them to scalar integrals using PV) but i was wondering how to do them without reducing them.
Look for instance at eq (3.9). If one is given such a type of integral but has no idea about...
Hi! Thanks for your reply!
I understand how to treat these integrals if the numerator of the integrand is expressed in terms of four-vectors. But how do I proceed if the numerator is written in the spinor bra-ket language above? I don't really know how to handle these expressions if the loop...
Hi guys,
i'm looking at one-loop calculations in terms of helicity spinor (basically a paper by Brandhuber, Travglini and others) language but i have no idea how to integrate them :)
For instance
\int FeynParam\int d^D L \frac{\langle a|L|b]^2}{(L^2-\Delta^2)^3}
How would I do...
Hi guys,
I have to brush up my knowledge about self-dual Yang Mills and I'm reading an ancient paper by Yang about it...and of course I'm stuck...although Yang writes 'it is easy to see that'...
Ok, so the self-duality condition of the YM field strength tensor is defined as...
Thank you for your answer! That is a nice way to understand this! From the book however I have the impression that the conclusion is much simpler to get and follows 'for free' from the invariance statements. But thanks a lot anyways!
earth2
P.s. you were right, the \sim should be an...
Hi guys,
i'm studying Conformal Field Theory using the big yellow book by Senechal et al. So far everything has been a smooth ride. I'm a bit stuck at the point where they derive the 2- and 3-point correlator for spinless fields.
Based on invariance under rotations and translations the...
Hi guys,
I'm under the impression that nowadays everything going on in hep-th is N=4 Susy stuff and that it has 20384093 awesome properties. Are there lecture notes where I can learn about all of that? I mean I know buzzwords but I don't see the whole picture. So, as I've said, are there...
Hey guys,
one quick question about Wick contractions and derivatives:
Suppose I want to write down all (non-vacuum) Wick contractions of two fields a, and one field A into a cubic QCD-like interaction term of the form
\partial^\nu A^{\mu, a}(p_1) a_\mu^b(p_2) a_\nu^c(p_3) f^{abc}
to...
Hey folks,
I've been stumbeling recently about new unitarity methods to obtain one-loop amplitudes by cutting them in all possible channels thereby reducing the full amplitude to products of tree amplitudes (pioneered by Bern, Dixon, Kosower, Dunbar).
From what I understand from my QFT...
Hi guys,
I'm a bit puzzled. I'm just reading some offline lecture notes where the Feynman rules of real (!) scalars coupled to gluons are given. However, with these rules the amplitude for phi g -> \bar{phi} g is considered. There are no further instructions. I'm just wondering how one can...
Hey guys,
say i have some standard propagators then I know how to combine them using Feynman's parameter method. But what do I do if one of these propagators is linear?
For instance:
\int d^Dk \frac{1}{(k-p)^2(k \cdot q)}
where q and p are some momenta. How do I combine them?
Does...
Does that even make sense on physical grounds? In any case it is not true since the cross section of pp collisions and ppbar collision is the same at high energies, so your argument breaks down.
Without being able to reproduce the full explanation, i think i remember that the increase has...
Concerning the increasing crosssection bit, there is a nice book by Forshaw and Ross called "Pomeron something something" (sorry, forgot the full title). Alternatively check http://arxiv.org/abs/hep-ph/9503226
Hope i could help!
earth2
Hey folks,
i have a question about LSZ and how to take into account the renormalization constants of the theory in question.
In the derivation, only the field strength renormalization enters as a factor of Z (or square root thereof) but some mates said that also the vertex renormalization...
Thanks for your reply!
So does that mean that if i write everything in terms of indices (like I did in my first post) I am in fact looking at the individual entries of the matrix, i.e. I'll deal with plain and simple numbers (may they be Grassmann or not)?
Hey guys,
something that puzzles me everytime I stumble across spinors is the following:
I know that i can express Dirac spinors in terms of2-component Weyl spinors (dotted/undotted spinors).
Now, if i do that, i can reexpress for instance the Lorentz or conformal algebra in terms of Weyl...
But look for instance at the completeness relation for spinors. It is nothing but
\slashed{P}= u^s\bar{u}^s with a sum over s. I.e. it is a matrix :) See Peskin Schröder in the beginning... :)
Thanks! But i don't get it if i look at it in terms of vectors and matrices...
So, u^s\bar{u}^s=4x4 matrix where u^r is a 1x4vector. How can i then have vector times matrix = matrix times vector?
Hey guys,
i'm stuck (yet again! :) )
I am somewhat confused by Dirac spinors u,\bar{u}. Take the product (where Einstein summation convention is assumed):
u^r u^s\bar{u}^s Is this the same as u^s\bar{u}^s u^r? Probably not cuz u^r is a vector while the other thing is a matrix, right...
Hey folks,
thanks for the replies so far. Let's look at a concrete example.
\int \frac{d^D l }{l^2(l-p)^2} with p^2=0. The integral is in principal trivial and gives approximately
\text{integral}=\Gamma(\epsilon)(1/p^2)^{2-d/2}. So in the case d=4-2\epsilon setting epsilon to zero I'll get...
Thanks fzero!
So, just to get this straight... if i put aside the aspect of renormalization for a sec on focus only on regularization: I calculate the integrals in d-dimension and then after integration set d to d=4 +/- 2epsilon. But which sign i use and if episilon is > 0 or <0 should not...
Hi!
Quick question: Does it make a difference if i choose my dim reg. to be D=4-2epsilon or D=4+2epsilon (i suppose in both cases epsilon >0).
I mean opinion i should not matter but standard qft books normally don't touch this question very deeply...
Cheers,
earth2