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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Field strength tensor written as commutator of covariant derivatives in QED
I am currently trying to understand the derivation of the relation
$$
\begin{equation}
F_{\mu\nu} = \frac{1}{iq}[D_{\mu}, D_{\nu}]\tag{1}\label{eq1}
\end{equation}
$$
in QED and I have trouble with ...
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Independence of $S$-matrix of $\xi$-gauge in QED
On page 298 in Peskin and Schroeder, the authors attempt to argue that the $S$-matrix should be independent of the $\xi$-gauge in QED. However, I don't understand their argument, in particular the ...
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Gauge theory of Electomagnetic Potentials - 2nd order derivatives
A quick introduction: In literature of electromagnetic theory, I saw little to no limitation on the formulating of an arbitrary gauge to the potential functions $(\phi,\vec{A})$. Perhaps it's required ...
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How to expand $(D_\mu\Phi)^\dagger(D^\mu\Phi)$ in $SU(2)$?
I would like to calculate the following expression:
$$(D_\mu\Phi)^\dagger(D^\mu\Phi)$$ where $$D_\mu\Phi = (\partial_\mu-\frac{ig}{2}\tau^aA_\mu^a)\Phi$$ and $A_\mu^a$ are the components of a real $SU(...
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What kind of object is a function in the context of gauge theory?
In the context of differential geometry, we have the Levi-Civita connection that tells us how to take derivatives of tensors. Two examples of the covariant derivative are
$$\nabla_\mu \phi = \partial_\...
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Gauge transformation rule for $dA$, where $A$ is the gauge field
Let $G$ be a non-Abelian simple compact gauge group and $\{ t^\alpha\}$ be a normalized set of generators for its Lie algebra $\mathfrak{g}$. Let $C^{\alpha \beta}_\gamma$ be the coupling constant for ...
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Writing gauge transformation of the gauge fields explicitly in terms of coordinates
Let $G$ be a non-Abelian simple compact gauge group and $\{ t^\alpha\}$ be a normalized set of generators for its Lie algebra $\mathfrak{g}$. Let $C^{\alpha \beta}_\gamma$ be the coupling constant for ...
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Derivation of the Noether current (Gauss law operator) in anomalous chiral gauge theory
I am reading Fujikawa-Suzuki's Path Integrals and Quantum Anomalies, §6.3. The Lagrangian I am looking at is
\begin{equation}
\mathcal{L}=-\frac{1}{4g^2}\left(\partial_\mu L_\nu^a-\partial_{\nu}L_\mu^...
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Causality for gauge dependent operators in quantum field theories
Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
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Unitary Gauge Removing Goldstone Bosons
The Lagrangian in a spontaneously broken gauge theory at low energies looks like
$$ \frac{1}{2} m^2 ( \partial_\mu \theta - A_\mu )^2 $$
and the gauge transformations look like $\theta \rightarrow \...
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Why are there no Goldstone modes in superconductor?
Usually, the absence of Goldstone modes in a superconductor is seen as an example of the Anderson-Higgs mechanism, related to the fact that there is gauge invariance due to the electromagnetic gauge ...
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2+1-dimensional $SU(N)$ Yang-Mills Theory
In recent years, there has been significant progress and growing interest in conducting quantum simulations of field theories using quantum devices. This typically involves formulating a Hamiltonian ...
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How to find a covariant gauge derivative from a field transformation
For reference: I'm self-studying from Peskin's Particle Physics 2019, which tries to sweep all QFT under the rug.
Consider an SU(3) gauge theory; I am told a $3\times 3$ scalar field $\Phi$ transforms ...
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How to do Variational Principle in QFT? ($SU(2)$-Yang-Mills)
I am currently familiarizing myself with QFT and have a question about this article. My understanding is that the Lagrangian density in (2) couples my gauge fields to the Higgs field. And with ...
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Reference request: scalar $O(N)$ gauge theory
I am interested in scalar $O(N)$ gauge theory and what you can do with it. Is there a standard reference section in a textbook/monograph/paper/whatever that has a decent overview?
Wikipedia has a ...