All Questions
Tagged with quantum-field-theory gauge-theory
725
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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
0
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1
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480
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Use of background field method
How do we use the background field method for renormalize a gauge theory?
3
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1
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403
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What is the "volume of the gauge group"?
I often see the term "volume of the gauge group" and I am not clear on what this is referring to. For example, in the second volume of Weinberg (page 22), he says
...the volume of the gauge ...
- 3,350
7
votes
3
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903
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How does the absence of quadratic terms in the Lagrangian imply massless quanta?
When studying gauge theory, I often see the statement that gauge invariance does not allow the Lagrangian of the theory to contain terms that are quadratic in the gauge field. For example, to quote ...
- 3,350
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0
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67
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Arbitrary heat kernel coefficients of covariant Laplacian with instanton
The heat kernel coefficients $b_{2k}(x,y)$ of the covariant Laplacian in an $SU(2)$ instanton background (for simplicity let's say $q=1$ topological charge, so the 't Hooft solution) on $R^4$ is ...
- 312
3
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1
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106
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Can we eliminate gauge degrees of freedom in QFT by quantizing the field strength directly?
In Matthew Schwartz's Quantum Field Theory and the Standard Model, he says (section 8.6, page 132) that it is possible to avoid introducing the redundant gauge degrees of freedom in QED by quantizing $...
- 3,949
5
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1
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107
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Is the Hamiltonian some sort of connection/gauge field?
I'm not sure if this is a well-defined question, but I was just looking through some old notes and noticed that the Hamiltonian in usual QM has a similar transformation as gauge fields in QFT: under ...
- 2,068
2
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1
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248
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Difference between Gauge invariance and BRST invariance
Which is the difference between gauge invariance and BRST invariance? Is it the same symmetry? Is the BRST the extention of the gauge symmetry even on the ghost fields?
- 159
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46
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Non-linear symmetry and symmetry at quantum level
Can anyone explain me what does the statement mean:
"the BRST symmetry is a non-linear symmetry, so the BRST is also a symmetry at the quantum level"?
What does "at the quantum level&...
- 159
2
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1
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121
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Magnetic field due to singular gauge transformation
In $SU(2)$ gauge theory over $\mathbb R^3$, consider the following gauge transformation (in spherical polar coordinates)
$$ \Omega=\begin{bmatrix}e^{i\phi}\cos(\theta/2)&\sin(\theta/2)\\-\sin(\...
- 742
3
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0
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180
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Witten anomaly and bound states of fermions
In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
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46
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Group factors in scalar-gauge box diagram
So, I'm currently writing my Thesis, which involves one-loop beta functions of a general $SU(N)$ for scalars and fermions fields, Yukawa coupling and one scalar self-coupling.
To this moment I was ...
- 21
3
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1
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180
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What does the dual gauge field have to do with topology?
The dual gauge field, $V$, is defined by $$^{\star}F(V)=F(A),$$ where $F$ is the field strength. The 't Hooft operator $\exp(i\int_C V)$ creates the trajectory of a magnetic particle along $C$. But I ...
- 742
1
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1
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131
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Why is the Gribov ambiguity not seen in perturbation theory?
I have read that the Gribov ambiguity doesn't appear in perturbation theory. Can anyone say why?
I found the following line in "Gribov copies and confinement" by
Anton Ilderton [1]:
Recall ...
- 742
0
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2
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157
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Explicit formula for a gauge transformation with winding number?
Does anyone know of an explicit expression for a gauge transformation, $\Omega:S^3\to G$, with a non-zero winding number (with $G=SU(n)$ say)?
- 742