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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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 ...
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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 ...
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Motivation for pure Yang-Mills Lagrangian
The Lagrangian for pure Yang-Mills theory is given by
$$-\frac14 F^{a\mu\nu}F^a_{\mu\nu} \tag{1}$$
where
$$F^a_{\mu\nu} = \partial_\mu A_\nu^a - \partial_\nu A_\mu^a + gf^{abc}A^b_\mu A_\nu^c.\tag{2}$$...
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Exactly what value does the Wilson line take?
Let $G$ be the Lie group of a given theory with the Lie algebra $\mathfrak{g}$.
According to the Wikipedia article, a Wilson line is of the form
\begin{equation}
W[x_i,x_f]= P e^{i \int_{x_i}^{x_f} A}
...
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
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Extracting a gauge-invariant variable from a given Wilson line? (NOT Wilson loop)
Let $W[x_i,x_f]$ be the Wilson line as defined here.
Under a local gauge transform $g(x)$, it transforms as
\begin{equation}
W[x_i,x_f] \to g(x_f)W[x_i,x_f] g^{-1}(x_i)
\end{equation}
which is shown ...
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Can Black Holes with electroweak or strong interactions exists in General Relativity or in Supergravity?
During my Master's degree, we studied Black Holes as solutions of Einstein-Maxwell equations, and I was wondering if it would be possible to also add strong or electroweak forces in the classic non-...
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Are Higgs mechanism and SSB different phenomena?
In the Standard Model, the Higgs mechanism is associated with the Spontaneous Symmetry Breaking (SSB).
My understanding is that it is the Higgs field which breaks the $SU(2) \times U(1)$ symmetry at a ...
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Does LQG break gauge invariance?
So, I'm working with another researcher on a possible connection between Loop Quantum Gravity (LQG) and String Theory (ST). My colleague is proposing and insisting on a action that is not WS ...
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Commutation in the Local Gauge Transformations
Let's say that I have a Unitary Local Gauge Transformation $U$, in which the Lie Generators are $T$:
$$ \partial_{\mu} U = \partial_{\mu} e^{-i T^{a} \alpha_{a}(x)} = U \partial_{\mu} \left( -i T^{a} \...
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Interpretation of self-interacting terms in the expansion of a pure YM Lagrangian?
Let $A^{\alpha}_\mu$ be the gauge field of a Yang-Mills theory where $\alpha$ is the gauge index of generators for some Lie algebra with structure constant $C_{\alpha \beta}^\gamma$ and $\mu$ is the ...
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Dirac field coupling to gauge fields
I've seen in couple sources that the gauge invariant Lagrangian for the Dirac field being written as follows:
$$\mathcal{L} = \frac{i}{2}[\bar{\psi}\gamma^{\mu}D_{\mu}\psi-(\bar{D}_{\mu}\bar{\psi})\...
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Masses of $SU(2)$ gauge bosons
I'm currently learning quantum field theory and I'm wondering one thing.The way I understood it is that in the $SU(2)$ Yang-Mills theory, all gauge bosons have the same mass due to the spontaneous ...
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Is color charge internal symmetry or global symmetry?
I was told the color charge in the standard model could not be observed directly. This sounded like the gauge field $\vec A$ in the electromagnetism. However, it is a discrete charge and does have ...
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Noether current for Yang-Mills theory in the absence of scalar field
The theory with an arbitrary compact gauge group $G$ is given. And global transformations are valid (see below)
$$
A_{\mu}\mapsto{A^{'}_{\mu}={\omega}A_{\mu}\omega^{-1}}
$$
also $\omega \in G$ and it ...
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Geometrical interpretation of gauge fields of spin other than 2
Gravitation can be interpreted as a gauge theory with a spin 2 graviton field. This graviton field in general relativity is also interpreter as a Riemannian metric. Do other gauge theories also have ...
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Topological behavior (or asymptotics at infinity) of gauge fields assumed in Fujikawa method
Chiral anomaly is computed very elegantly by Fujikawa method, which is also presented in Section 22.2 of Weinberg QFT textbook volume 2 or wikipedia.
Here, the underlying spacetime is assumed to be $\...
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Non-abelian Yang-Mills in 1+1 dimensions
Abelian electrodynamics in 1+1 dimensions is solvable, in the sense that we can find the space of solutions for the equation of motions $\partial_\mu F^{\mu\nu}=0$. To see this, one first notice that ...
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Gauge Theory: Mathematics + Physics [duplicate]
I'm interested in learning mathematical gauge theory, particularly its applications in physics, focusing on (topological) quantum field theory with an emphasis on condensed matter.
I'm looking for ...
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Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
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Visualization of a gauge field with non-null winding number
In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
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Chern-Simons (K matrix) theory and ${\rm Spin}^{\mathbb C}$ connections
If I understand correctly (e.g. from this paper), an Abelian bosonic Chern-Simons theory defined on $T^2\times \mathbb R$ is specified by a $K$ matrix via e.g. $S \sim \int_M K_{IJ}A^I \wedge dA^J$. ...
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Significance of the phase of the condensate as compared to that of the regular Fermi sea in the Anderson-Higgs mechanism
I do not fully understand how the phase of the charged Cooper pair condensate is different from the phase of e.g. the Fermi liquid in a regular metal.
The state of the metal (any quantum state really) ...
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