# Questions tagged [gauge-theory]

A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

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### Photon Path Integral and Lorenz Gauge

I am reading Srednicki's QFT book (http://web.physics.ucsb.edu/~mark/qft.html). In chapter 57, specifically in page 343, the book stated that there's a problem with the path integral because the ...
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### How to understand the path integral of $U(1)$ gauge field under Coulomb gauge?

I want to obtain Green's function of $U(1)$ gauge field under Coulomb gauge. For some reason, I want to finish it in Euclidean space, i.e. both time-space $x_\mu$ and field strength $A_\mu$, so that ...
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### How to compute gauge potential $A$ from the field strength $F$?

Let $F=dA+A \wedge A$ be the field strength that solves vaccum Yang-Mills equation. The question is: how to recover the gauge potential $A$? Is there any standard way? or any theorem stating the ...
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### Variation of QED gauge missing step

I have several questions about this problem. I have been given a non-linear gauge condition for a QED theory: $$F = \partial_{\mu}A^{\mu} + \frac{\lambda}{2}A_{\mu}A^{\mu}.$$ I have found online that ...
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### Non-linear QED gauge fixing, writing the effective Lagrangian

I have several questions about this problem. I have been given a non-linear gauge condition for a QED theory: $$F = \partial_{\mu}A^{\mu} + \frac{\lambda}{2}A_{\mu}A^{\mu}.$$ Then I need to write the ...
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### Is this measure employed in the Faddeev-Popov procedure related to the Haar measure?

In the Faddeev-Popov procedure one defines the Faddeev-Popov determinant through the formula $$\int {\mathcal{D}\alpha \ } \delta\big[G(A^\alpha)\big]\Delta[A]=1,\tag{1}$$ where $G(A^\alpha)$ is the ...
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### Calculations of chiral condensate (from David Tong's notes)

I got confused on the calculation of chiral condensate in David Tong's Gauge theory. The equation 3.52 reads \begin{equation} \langle\bar{\psi}_{-}\psi_{+}\rangle=\big(\prod_{n}\lambda_n\big)\frac{1}{...
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### Interpretation of QED as a $U(1)$ gauge theory

Forgive me if what I’m asking is too naive for this site. I'm a math student who is recently studying electrodynamics and gauge theory myself. While I'm aware of the fact that QED can be realized as a ...
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### Writing the $U(1)$ gauge transformation as coordinate transformation

In quantum mechanics one can "always" write the way an operator acts on a wave function as a coordinate transformation. As an example we can look at unitary representation of the momentum ...
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### What is $D$ or $D$-with-a-slash-through-it in the Standard Model equation(s)?

In the mathematical formulation of the Standard Model, which I do not understand yet, there is a capital letter $D$ or $D$-with-a-slash-through-it that I can't find an explanation for. Flip Tanedo (a ...
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### Does one ever need infinitely many cohomologies?

In a theory containing gauge fields or higher-form gauge fields, if the background spacetime is a complicated manifold, a nice way to represent the configuration of the gauge field mathematically is ...
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### Maxwell solution in differential forms

Maxwell equation's in differential form: $dE = 0 \ and\ \ (\ast d \ast)E = p$ in static situation. Where $E \in \Omega^1(U)$, $p \in \Omega^0(U)$, $\ast$ is hodge star operator, $U= \mathbb{R}^3$ ...