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# 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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### Comparator operator in QFT

In Peskin and Shroeder, for a local $U(1)$ transformation, the comparator operator is expanded as: U(x+\epsilon n, x) = 1 -ie\epsilon n^{\mu}A_{\mu} + \mathcal{O}(\epsilon^2) \tag{15....
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### What happens to the symmetry after gauge fixing?

Given a theory with gauge symmetry. After gauge fixing where does the symmetry go? Does the gauge symmetry turn into a global symmetry? For example there is a way to quantize fields theory with BRST ...
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### Calculating $S$-matrix in string theory

To calculate string $S$-matrix, we mainly use Faddeev-Popov gauge fixing method, as in chapter 6 of Polchinsky's book 《string theory》. But in section 6.2, 'tree level amplitude', I didn't find ...
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### Question about the Lie group $SU(3) \times SU(2) \times U(1)$ and the concept of manifold

I don't know if this question is a duplicate, so I'll delete if is. Well, I'm in the very beginning of the study of contemporary topics such as gauge theories, I would say that I'm in a "science ...
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### Delta function conversion into gauge-fixing Lagrangian in the path integral

So, I am at the moment working on gauge-fixing a path integral. The procedure involves adding a delta function $\delta g$ to the path integral (together with the faddeev-popov determinant, but that is ...
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### What are emergent gauge fields in condensed matter physics?

My background: I have a very little knowledge about topological insulators. Medium level knowledge of Quantum mechanics and linear algebra. Almost no knowledge about Field Theories. I have studied ...
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### $1/4$ coefficient in QED Lagrangian [duplicate]

What is the reason 1/4 coefficient in the tensor multiplication of the electromagnetic field strength? $$\mathscr{L} = -\, \frac{1}{4} \, F_{\mu \nu} \, F^{\mu \nu}. \tag{1}$$
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Given some theory described by fields from a vector bundle $E$, with section $\phi \in \Gamma(E)$, we get that transformations on the fields are part of the automorphisms on that bundle, ie, $\Phi \in ... 0answers 27 views ### Is there a specific structure to the automorphism set of a field theory with respect to internal v. spacetime symmetries? I'm trying to work out what it means exactly for a field to be transformed, without referring to gauges for now. As far as I can tell, from a rigorous perspective, a transformation of the field is an ... 1answer 155 views ### What classifies gaugings? Gauging a global symmetry$G$introduces several free parameters to the theory. For example, In$d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ... 2answers 90 views ### Why define$D_\mu = \partial_\mu -ieA_\mu$with the electric charge$e$? If$D_\mu = \partial_\mu - ieA_\mu$then the QED Lagrangian is invariant under $$A_\mu \to A_\mu + \frac{1}{e}\partial_\mu\alpha(x)$$ $$\psi \to e^{i\alpha(x)}\psi$$ However if$D_\mu = \partial_\mu -...
For example, consider the electromagnetic theory given by \begin{align} I=-\frac{1}{4}\int d^4x\, F_{\mu\nu}F^{\mu\nu}, \end{align} where $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$. The action ...