All Questions
41
questions
3
votes
0
answers
74
views
Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
1
vote
0
answers
39
views
Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
1
vote
0
answers
58
views
Unitarity and renormalizability in $R_\xi$ and 't Hooft gauge
Consider the massive propagator with gauge fixing $\frac{1}{2a} (\partial A)^2$
$$
\Delta_{\mu\nu}=-i\left[\frac{g_{\mu\nu}}{k^2-m^2}-\frac{k_\mu k_\nu}{m^2}\left(\frac{1}{k^2-m^2}-\frac{1}{k^2-am^2}\...
0
votes
0
answers
26
views
Question on the Proof of Renormalizability in Gauge Field Theory in Collins's *Renormalization*
I am currently reading Collins's Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion, and have reached Chapter 12. However, I am puzzled ...
1
vote
1
answer
88
views
Perturbative expansion and renormalization of non-abelian Yang-Mills theory solely in terms of gauge-invariant quantities?
In standard QFT, each term in the perturbative expansion for a gauge theory is not necessarily gauge-invariant. Only the whole sum of Feynman diagrams is guaranteed so.
However, at least for QED, ...
4
votes
1
answer
130
views
Why is $Z_3= Z_\xi$ in a non-abelian gauge theory?
In my lecture notes for a course on QFT it is said that, also in non-abelian gauge theories, the identity $Z_3 = Z_\xi$ holds, where those renormalization parameters belong respectively to the ...
0
votes
1
answer
480
views
Use of background field method
How do we use the background field method for renormalize a gauge theory?
1
vote
0
answers
46
views
Group factors in scalar-gauge box diagram
So, I'm currently writing my Thesis, which involves one-loop beta functions of a general $SU(N)$ for scalars and fermions fields, Yukawa coupling and one scalar self-coupling.
To this moment I was ...
3
votes
1
answer
249
views
Fermion self-energy and vertex renormalization in Non-Abelian Gauge Theories
I am currently going through chapter 16 of Peskin and Schroeder and some of the calculations seem very obscure to me. The problems are as follows:
On page 528, the authors compute the value of the ...
1
vote
0
answers
210
views
Question on the Background Field Method for Non-Abelian Gauge theory
I am reading Peskin's and Schroeder's book "An Introduction to Quantum Field Theory". In Chapter 16.6 the authors use the Background Field Method to determine the $\beta$ function for a non-...
3
votes
0
answers
41
views
Regularization scheme independence as a gauge redundancy?
Observables should not depend on the regularization scheme under some renormalization procedure. Is there some way to interpret this fact as a gauge redundancy? In particular, is there some group ...
2
votes
0
answers
59
views
Gauge transformation in Background Field Gauge, Weinberg Section 17.4, QFT 2
Whole idea of using background field method is to keep explicit gauge invariance, which is useful during renormalization.
In section 17.4, background field gauge, Weinberg defines a ...
0
votes
0
answers
96
views
Can we make a massive non-abelian gauge field renormalizable by gauge fixing without Higgs mechanism?
There have been a lot of similar questions about this topic on this website, such as Gauge invariance is just a redundancy. Why is massive abelian gauge field renormalizable but massive non-abelian ...
0
votes
0
answers
43
views
Effective Action behaviour in $SU(N)$ Gauge Theory in Solodukhin
In Solodukhins paper https://arxiv.org/abs/0802.3117
he says that the effective Action of a 4D CFT has the general structure:
$$W = \frac{a_0}{\epsilon^4} +\frac{a_1}{\epsilon^2}+a_2 \ln{\epsilon} +\...
3
votes
1
answer
687
views
Gauge invariance of scalar QED
Let's consider a complex $\phi$ coupling minimally to $U(1)$ gauge field:
$$
\mathcal{L} = - \frac{1}{4} F_{\mu\nu} F^{\mu\nu} + (D_\mu\phi)^*(D^\mu\phi) - m^2 \vert\phi\vert^2 + \dots
$$
For now, I ...