Skip to main content

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.

Filter by
Sorted by
Tagged with
2 votes
0 answers
27 views

Do all magnetic monopole models always imply higher symmetry than regular EM?

First, Maxwell equations do not say that magnetic monopoles do not exist. The equations can easily be generalized to include magnetic monopoles. What I want to know is. Do ALL magnetic monopole ...
Jtl's user avatar
  • 445
1 vote
1 answer
56 views

Gauss law, gauge and global symmetries

I am reading Witten's paper on the confinement/deconfinement phase transition in $\mathcal{N}=4$ $\mathrm{SU}(N)$ SYM theory. I am a bit stuck at section "Confinement" at Finite Volume, page ...
Davide Morgante's user avatar
0 votes
0 answers
29 views

Second-order perturbations of gauge field in GR

When expanding a Lagrangian $\mathcal{L}[g_{\mu\nu},A_\mu,\chi]$ to second order in perturbations, the metric is expanded like $$g_{\mu\nu}\to g_{\mu\nu}+\delta g_{\mu\nu}+\frac{1}{2}\delta g_{\mu}^{\,...
furious.neutrino's user avatar
1 vote
0 answers
22 views

Derivation of the BRST invariance in QCD

I am trying to follow the proof for the BRST invariance in QCD in the following pdf file: https://scipp.ucsc.edu/~haber/ph222/BRST.pdf (section 3, from end of page 6) I can understand the derivations ...
Ahnel's user avatar
  • 11
0 votes
3 answers
37 views

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 ...
Hunic99's user avatar
3 votes
1 answer
58 views

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 ...
User3141's user avatar
  • 863
2 votes
2 answers
74 views

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 ...
AmnonJW's user avatar
  • 21
0 votes
1 answer
102 views

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(...
Hendriksdf5's user avatar
1 vote
1 answer
53 views

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_\...
dolefeast's user avatar
  • 170
0 votes
1 answer
74 views

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 ...
Keith's user avatar
  • 1,669
0 votes
2 answers
59 views

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 ...
Keith's user avatar
  • 1,669
1 vote
0 answers
35 views

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^...
Archi's user avatar
  • 29
2 votes
1 answer
56 views

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 ...
Ervand's user avatar
  • 43
0 votes
0 answers
37 views

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 \...
infinity's user avatar
5 votes
2 answers
378 views

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 ...
cx1114's user avatar
  • 109
0 votes
3 answers
224 views

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 ...
Quantization's user avatar
2 votes
1 answer
63 views

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 ...
spiderhouse's user avatar
0 votes
0 answers
71 views

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 ...
Hendriksdf5's user avatar
1 vote
1 answer
53 views

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 ...
2 votes
1 answer
94 views

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 ...
CBBAM's user avatar
  • 3,350
2 votes
3 answers
148 views

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 $$F^a_{\mu\nu} = \partial_\mu A_\nu^a - \partial_\nu A_\mu^a + gf^{abc}A^b_\mu A_\nu^c.\tag{2}$$...
CBBAM's user avatar
  • 3,350
0 votes
0 answers
50 views

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} ...
Keith's user avatar
  • 1,669
3 votes
0 answers
74 views

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 \...
ChungLee's user avatar
2 votes
0 answers
59 views

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 ...
Keith's user avatar
  • 1,669
3 votes
1 answer
73 views

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-...
Aleph12345's user avatar
3 votes
1 answer
97 views

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 ...
Keith's user avatar
  • 1,669
2 votes
0 answers
69 views

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 ...
Luigi Teixeira de Sousa's user avatar
0 votes
1 answer
46 views

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} \...
user avatar
4 votes
1 answer
117 views

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 ...
Keith's user avatar
  • 1,669
1 vote
1 answer
64 views

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})\...
physics_2015's user avatar
2 votes
0 answers
68 views

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 ...
Hendriksdf5's user avatar
0 votes
1 answer
47 views

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 ...
ShoutOutAndCalculate's user avatar
0 votes
0 answers
67 views

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 ...
drxvmrz's user avatar
  • 11
1 vote
1 answer
73 views

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 ...
Andreas Christophilopoulos's user avatar
2 votes
1 answer
85 views

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 $\...
Keith's user avatar
  • 1,669
2 votes
1 answer
88 views

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 ...
BVquantization's user avatar
2 votes
0 answers
58 views

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 ...
1 vote
0 answers
39 views

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}...
quantumology's user avatar
0 votes
1 answer
59 views

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 ...
Gabriel Ybarra Marcaida's user avatar
0 votes
0 answers
36 views

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. $S \sim \int_M K_{IJ}A^I \wedge dA^J$. ...
Joe's user avatar
  • 186
-1 votes
1 answer
46 views

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) ...
Rooky's user avatar
  • 21
1 vote
0 answers
43 views

Non-invertible symmetries: Half gauging and 't Hooft lines

In (2.27) of https://arxiv.org/abs/2205.05086, when performing a gauge transformation of the background gauge field $B \to B +d \Lambda $, the 't Hooft line $H(\gamma)$ transforms as \begin{equation} ...
superyangmills's user avatar
1 vote
0 answers
58 views

Unitarity and renormalizability in $R_\xi$ and 't Hooft gauge

Consider the massive propagator with gauge fixing $\frac{1}{2a} (\partial A)^2$ $$ \Delta_{\mu\nu}=-i\left[\frac{g_{\mu\nu}}{k^2-m^2}-\frac{k_\mu k_\nu}{m^2}\left(\frac{1}{k^2-m^2}-\frac{1}{k^2-am^2}\...
Tanmoy Pati's user avatar
2 votes
1 answer
62 views

Abelian Chern-Simons large gauge transform

My question concerns the $U(1)$ Chern-Simons theory with the action $$S = \frac{k}{2\pi}\int A\wedge \mathrm{d}A.$$ In my lecture, it is stated that: A large gauge transformation involves taking $A\...
shamwowexcitante's user avatar
0 votes
0 answers
20 views

In the local $U(1)$ symmetry , does the inverse projection map of each point is onto the tangent plane at the point?

Does a $U(1)$ local symmetry on a non-flat spacetime, say a sphere, imply that a point on the sphere is equivalent to a circle (corresponding to the phase) on the tangent space to that point? Does ...
Eden Zane's user avatar
  • 251
0 votes
2 answers
124 views

Meaning of “transforms like the adjoint” in the context of Yang Mills Theory and connection to Lie Algebra

In Srednicki Chapter 69, we say something transforms like the adjoint if its transformation under the $SU(N)$ group action is $$W\rightarrow UWU^\dagger$$ The Field strength and the covariant ...
JohnA.'s user avatar
  • 1,713
1 vote
0 answers
32 views

Connection between Noether's theorem for gauge theories and 1-form symmetries?

Applying Noether's theorem to a gauge theory, one can show that the conserved current is generically of the form $$J^\mu=\partial_\nu k^{[\mu\nu]},$$ such that the conserved charge is really ...
arow257's user avatar
  • 1,055
2 votes
2 answers
91 views

Effect of gauge-fixing via Lagrange multipliers on Euler-Lagrange equations

Preamble Consider the Lagrangian density for electrodynamics: $$L=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^\mu\tag{1}$$ With the usual definition of $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$...
Matt Dickau's user avatar
1 vote
1 answer
47 views

Counting of degrees of freedom in Higher Spin Theories in curved spacetime

In 4d Minkowski, a (bosonic) tensor field with spin $s\in\mathbb{N}_+$ are constrained by Poincaré symmetry, and the physical degrees of freedom can be counted by considering the little group: a spin-$...
Physics Cat's user avatar
4 votes
1 answer
74 views

Can we impose Coulomb gauge without using temporal gauge in source-free Maxwell electrodynamics?

Coulomb gauge is $$\vec{\nabla} \cdot A=0$$ Now, from expression for electric field in terms of potentials $\vec{E}=-\vec{\nabla} \phi-\frac{\partial \vec{A}}{\partial t}$ and Gauss Law $\vec{\nabla} \...
Nairit Sahoo's user avatar

1
2 3 4 5
49