All Questions
Tagged with gauge-theory renormalization
58
questions
3
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0
answers
74
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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
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
- 51
1
vote
0
answers
39
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Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
- 81
1
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0
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58
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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}\...
- 534
0
votes
2
answers
124
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Renormalizability of Quantum Gravity
At the end of chapter 6 on p. 210 in David's Griffiths' book Introduction to Elementary Particle Physics he says that 't Hooft proved that all gauge theories are renormalizable. I have also read ...
- 25
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26
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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 ...
- 51
1
vote
1
answer
88
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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, ...
- 1,669
2
votes
0
answers
45
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How does spin $j$ matter contribute to the running of the gauge coupling?
The one-loop beta function $\beta(g)$ for the gauge coupling $g$ with gauge group $G=SU(N_c)$, in a theory with $n_f$ spin-1/2 fermions in a representation $R_f$ of $G$, and $n_s$ complex scalars in a ...
- 3,514
4
votes
1
answer
130
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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 ...
- 307
0
votes
1
answer
480
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Use of background field method
How do we use the background field method for renormalize a gauge theory?
0
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0
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244
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One-loop renormalization of the gauge coupling
Quoting Yuji Tachikawa, chapter 3 of "${\cal N}=2$ Supersymmetric Dynamics for Pedestrians":
Recall the one-loop renormalization of the gauge coupling in a general Lagrangian field theory $$...
user242231
1
vote
0
answers
46
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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 ...
- 21
3
votes
1
answer
249
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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
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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-...
- 3,992
3
votes
0
answers
41
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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 ...
- 3,514
2
votes
0
answers
59
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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 ...
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