All Questions
55
questions
2
votes
1
answer
92
views
Understanding the Gaussian weight and the parameter $\xi$ when quantizing gauge theories
In section 9.4 of Peskin & Schroeder's textbook on quantum field theory, when applying the Faddeev Popov procedure to quantize an Abelian gauge theory, they obtain the following functional ...
- 3,350
1
vote
0
answers
32
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A reference request on fundamental modular domains in the context of Gribov ambiguity
I see that there are some references in the post PE on the Gribov ambiguity.
However, resolution of this ambiguity, as stated in wiki, is to find the fundamental modular region (FMR).
I looked into ...
1
vote
0
answers
69
views
Faddeev-Popov Method for Gauge Fixing in CFT (Light-ray Operators)
I was attempting to go through the paper by Petr Kravchuk and David Simmons-Duffin: https://arxiv.org/abs/1805.00098 where I encountered the following
Just below E.4, it is mentioned that for the ...
- 41
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 ...
- 307
3
votes
1
answer
237
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Temporal Gauge with periodic boundary conditions
In Yang-Mills theory with periodic boundary conditions in time, is the temporale gauge, i.e. $A_0 = 0$, well defined?
Periodic boundary conditions would be
$$A_\mu(T_2,x) = A_\mu(T_1,x).$$
Naively I ...
- 2,263
1
vote
0
answers
26
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Proving that the Faddeev-Popov path integral is independent of the gauge choice? [duplicate]
I know that the Faddeev-Popov path integral is gauge invariant. But how does one show that
\begin{equation}
I = \int \mathcal{D}\mathcal{A}_\mu \bigg|\frac{\delta\mathcal{G}}{\delta{\omega}}\bigg|\...
- 904
5
votes
1
answer
333
views
QED scattering cross sections are independent of the gauge-fixing terms
In QED, the Lagrangian with gauge-fixing terms is $$\tag{7.2}L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\frac{1}{2}\xi(\partial^\sigma A_\sigma)^2 $$ (See Greiner field quantization), from which we can obtain ...
- 789
1
vote
0
answers
159
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Peskin and Schroeder's QFT eq.(9.56)
On Peskin and Schroeder's QFT book, page 296, the book give the functional integral formula after inserting Faddeev and Popov's trick of identity.
$$ \int \mathcal{D} A e^{i S[A]}=\operatorname{det}\...
- 1,421
0
votes
0
answers
67
views
Unitarity gauge
Weinberg in Chapter 21, section 21.1, QFT 2, says that, in unitarity gauge $\tilde{\phi}_n(x) = \gamma^{-1}_{nm}(x)\phi_m(x)$,
we do not have degrees of freedom with negative probability, like time-...
- 433
1
vote
0
answers
86
views
Commutator of gauge field and the scalar field in the Stueckelberg Lagrangian with gauge-fixing terms
I was trying to add a gauge fixing term to Stueckelberg Lagrangian and cancel the mixing term between scalar $\chi$ field and vector $A_\mu$ field.
$${\cal L}_{Stueckelberg} = -\frac{1}{4}V_{\mu\nu}V^{...
- 139
5
votes
1
answer
414
views
The Faddeev-Popov generating functional and its independence on the gauge-fixing function
A technical question on the Faddeev-Popov procedure (P&S Chapter 9). P&S introduce the functional integral, which is equal to one and then they choose the gauge-fixing function $G(A)$ to be ...
- 3,992
7
votes
1
answer
533
views
Why is quantizing the free electromagnetic field in the Lorenz gauge more subtle than in the Coulomb gauge?
Quantizing the free electromagnetic field in the Lorenz gauge, $\partial_\mu A^\mu=0$, is subtle. We must add a gauge-fixing term to the action so that $\pi^0$ does not vanish identically. Also, we ...
- 11.8k
0
votes
0
answers
64
views
Steps in Quantizing Electromagnetic Field for the Gauge Condition $A_0=0$
While reading section 9.3 of QFT An Integrated Approach by Fradkin, it is shown (see equations $(9.49)$ and $(9.54)$ of the book)
$$B_{j}(\boldsymbol{x})^{2}=\boldsymbol{p}^{2} A_{j}^{T}(\boldsymbol{p}...
- 381
6
votes
1
answer
225
views
A relationship between the proof of a renormalizability and gauge fixing conditions?
I already know that QCD is renormalizable in several gauges, including the $\xi$ gauge and the background field gauge. That is, the divergence of the quantum effective action is limited by symmetry, ...
- 1,363
3
votes
1
answer
201
views
The residual gauge symmetry of Yang-Mills theory after Wick rotation
I am a bit puzzled by a statement in this question here. In particular, the claim that the residual gauge symmetry in Yang-Mills theory disappears upon Wick rotation to the Euclidean theory.
For ...
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