Tagged Questions
5
votes
0answers
72 views
Setting of renormalization scale in field theory calculations
In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
5
votes
1answer
69 views
Significance of Poles of Correlation Function in QFT
In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
2
votes
1answer
68 views
Alternative methods to derive the static potential in the NR limit of QED
In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level ...
6
votes
1answer
127 views
Database of scattering amplitudes
I want to check whether my result for the invariant amplitude of the electron-electron scattering (to lowest order in $\alpha$; t+u channels) is correct or not.
I can't find any reference that has ...
5
votes
2answers
217 views
Can scattering amplitudes be simplified with 1PI diagrams?
I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
1
vote
1answer
150 views
Integral in Peskin and Schroeder
I'm having a bit of a slow day, and can't see how to do the following integral in Peskin and Schroeder (page 107 for anyone with the book). We've derived in the centre of mass frame the integral over ...
2
votes
1answer
149 views
Scattering Processes in Scalar Yukawa Theory
I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through ...
3
votes
0answers
124 views
Inclusion of information about external particles to calculate scattering amplitudes
In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states
$$ A = \int\limits_{\rm{life time}} d\tau ...
1
vote
1answer
296 views
Feynman Rules for massive vector boson interactions
I am stuck at the beginning of a problem where I am given an interaction term that modifies the regular QED Lagrangian. It involves the interaction between a photon field and a massive vector boson: ...
0
votes
1answer
101 views
Scattering Amplitudes in Centre of Mass Frame
I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be
...
3
votes
1answer
91 views
Is the Møller wave operators $\Omega_\pm$ related to $\lim_{t\rightarrow\infty}U(t)$ of field theory?
When we want to compute correlation functions $\langle\Omega|\,T\hat{\phi}(x_1)\ldots|\Omega\rangle$ in an interacting quantum field theory, we relate it to the free-field objects $|0\rangle$ and ...
2
votes
2answers
251 views
Scalar Field Redefinition and Scattering Amplitude
Consider a field redefinition
$$
\phi \rightarrow \phi' = \phi+\lambda \phi^2
$$
Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
8
votes
2answers
401 views
What is the physical interpretation of the S-matrix in QFT?
A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers.
Given a quantum field theory when ...
7
votes
1answer
249 views
When we define the S-matrix, what are “in” and “out” states?
I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with
$$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle
=
S^{-1}
...
6
votes
1answer
408 views
Proof of Yang's theorem
Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
2
votes
1answer
97 views
scattering singularity
In QFT when one works out the cross section between two colliding electrons one gets a formula which is proportional to $\theta^{-4}$ where $\theta$ is the scattering angle which is due to a nearly ...
3
votes
2answers
151 views
Radiative Corrections and Bremsstrahlung
I am having trouble understanding why it is consistent to include "Breamsstrahlung" diagrams in computations of scattering amplitudes.
For example, consider the scattering of two electrons to two ...
4
votes
1answer
201 views
A certain gluon scattering amplitude
I am stuck with this process of calculating the tree-level scattering amplitude of two positive helicity (+) gluons of momentum say $p_1$ and $p_2$ scattering into two gluons of negative (-) helicity ...
3
votes
1answer
204 views
Spinor integration
I am learning on-shell methods for one loop integrals from this paper: Loop amplitudes in gauge theory: modern analytic approaches by Britto. Starting with formula (18) spinor integration is ...
6
votes
1answer
78 views
Some more questions about the BCFW reduction
This question is a continuation of this previous question of mine and I am continuing with the same notation.
One claims that one can actually split this $n$-gluon amplitude such that there is just ...
5
votes
1answer
107 views
Some questions about the BCFW reduction
I am trying to give a fast sketch of what the BCFW reduction does and embed within it some questions at the steps which I don't seem to understand clearly. The first bullet point is sort of a very ...
4
votes
3answers
350 views
Unitarity of S-matrix in QFT
I am a beginner in QFT, and my question is probably very basic.
As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix ...
7
votes
4answers
207 views
Different kinds of S-matrices?
It seems to me that the notion of an "S-matrix" refers to several different objects
One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
2
votes
1answer
222 views
How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments?
How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments? I am having a hard time figuring the answer out. Please help.
2
votes
2answers
293 views
Physical interpretation of infinite total cross section
What does it tell us about a process, say A+B->C+D, if the calculated total cross section is infinite?
2
votes
1answer
86 views
Cross sections and renormalization scheme
Can the result on cross section of some process be dependent on the renormalization scheme used?
12
votes
4answers
450 views
Tree level QFT and classical fields/particles
It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
5
votes
1answer
118 views
diffusion by an external potential in quantum field theory
I'm studying quantum field theory and I encountered some problems of diffusion of particles by an external potential. Until now I have to do with diffusion of the type particle-particle obtaining the ...
7
votes
1answer
264 views
How do ideas of leading singularities and Grassmanian help in curing infrared divergences when calculating N=4 scattering amplitudes?
Broadly speaking how do ideas of leading singularities and Grassmanian help in curing infrared divergences when calculating N=4 scattering amplitudes? My understanding is that one gets infra red ...
22
votes
3answers
1k views
Scattering of light by light: experimental status
Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
