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Questions tagged [gauge]

Use this tag to discuss gauge-fixing conditions, as in the phrase 'choosing a gauge', such as, e.g. the Lorenz gauge, Coulomb gauge, Feynman gauge, Landau gauge, axial gauge, temporal gauge, light cone gauge, etc.

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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 ...
User3141's user avatar
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11 votes
2 answers
513 views

Why is nonzero net charge density incompatible with the cosmological principle?

In an answer to a question about the overall charge-neutrality of the universe, benrg writes, A nonzero net charge density is incompatible with the cosmological principle. Unlike the gravitational ...
rob's user avatar
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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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Independence of $S$-matrix in QED of a gauge of EM field

Due to existence of several ways to fix a gauge of an EM field in QED, there are several ways to quantize it. That leads to non-uniqueness of photon propagator and hence to non-uniqueness of integrals ...
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1 answer
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Green's function solution in 2D for the potential of solenoids in the Lorenz gauge

My main goal is to find a general expression for the potential in the Lorenz gauge of some solenoidal (not necessarily circular) current density using the Green's function. I assume that the current ...
Arceon's user avatar
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How is Wald deriving this Gauge condition: $\partial^b\, \overline{\gamma}_{ab} = 0$?

R. Wald in Section#4.4 of his book General Relativity derives the EFE in the case of a weak gravitational field by taking the curved spacetime metric $g_{ab}$ to be a "small" perturbation $\...
math-physicist's user avatar
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
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 vote
1 answer
73 views

Gravitational waves from metric perturbation

I have just been introduced to gravitational waves from metric perturbations and I have some questions about gauge symmetry and solutions in a given gauge. Consider a metric on the form $g_{\mu\nu} = \...
ICOR's user avatar
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How was the $\Gamma _\mu$ be used as a gauge condition in the Generalized Harmonic formulation $R_{\mu\nu}$

I'm watching a video(ICTP-SAIFR Numerical Relativity by Sascha Husa) where he mentioned that $$R_{\mu\nu} =-\frac{1}{2} g^{\lambda \rho} g_{\mu\nu,\lambda \rho} +\nabla_{ (\mu }\Gamma_{\nu)} +\...
ShoutOutAndCalculate's user avatar
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Degree of freedom - Lorentz transfomation reduces it? [duplicate]

I am having a real difficult to counting degree of freedom. In fact, I notice that sometimes I am confused about what exactly we count as DoF, and what we do not count. See, for example, the ...
LSS's user avatar
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Counting degrees of freedom in theories with two-forms [duplicate]

I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
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Gauge redundancy and Gauge fixing

Take any gauge invariant theory, for instance QED. The QED Lagrangian is invariant under $$A_{\mu}(x)\rightarrow A'_{\mu}(x)=A_{\mu}(x)+\partial_{\mu}. \alpha(x)$$ I have chosen a local gauge ...
schris38's user avatar
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1 vote
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A reference request on fundamental modular domains in the context of Gribov ambiguity

I see that there are some references in the post PE on the Gribov ambiguity. However, resolution of this ambiguity, as stated in wiki, is to find the fundamental modular region (FMR). I looked into ...
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1 answer
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Problems about "boundary conditions and topology"

In the book Field Theories of Condensed Matter Physics by Fradkin In Page 311, when discussing the effects of boundary conditions on $Z_2$ lattice gauge theory, in the weak coupling phase, Fradkin ...
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Can the Coulomb potential as the vacuum energy shift in QED also be calculated with a field quantized in the Coulomb gauge?

This answer explains how the Coulomb-potential can be calculated as the energy shift of the (photon) ground state for 2 charges fixed in place. This calculation has been done for a covariant "...
Quantumwhisp's user avatar
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1 answer
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Magnetic vector potential in 1+1 spacetime dimensions

In the theory of electromagnetism in 1+1 spacetime dimensions (one temporal and one spatial coordinate), one can define the 2-potential vector (analogous to the 4-potential vector in 3+1 spacetime ...
Daniel Vainshtein's user avatar
7 votes
2 answers
331 views

Is the electromagnetic 4-potential a Lorentz 4-vector in the Coulomb gauge?

In the course of Classical Electrodynamics I learned that in the Lorenz gauge it is easy to prove that the 4-potential $A$ is a 4-vector, that is its components $A^\mu=(\phi/c,\vec{A})$ transform as ...
Danilo Lombardo's user avatar
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Can we express the electrodynamic potentials $V$, $\mathbf{A}$ in terms of the electrodynamic fields $\mathbf{E}$, $\mathbf{B}$?

In Griffiths' Introduction to Electrodynamics problem 10.25, I am asked to draw a "triangle diagram" illustrating the relationship between (1) the sources $\rho$, $\mathbf{J}$, (2) the ...
Jonathan Huang's user avatar
1 vote
0 answers
31 views

Expression for the gravitational-wave energy-momentum tensor without choosing a gauge

While studying section 7.6 of Carroll's introduction to general relativity, I encountered difficulties deriving equation 7.165 for the gravitational-wave energy-momentum tensor. Unfortunately, I was ...
bruno henrique's user avatar
1 vote
1 answer
76 views

Virasoro constraint under the static gauge

I am reading an article on introduction to string theory. Consider an open string of length $L$, rotating around its center of mass with angular velocity $\omega$. Here we fix the gauge by the static ...
user174967's user avatar
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1 answer
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Solving for gluon propagator in axial gauge

I know the two-point function is given by: $$ \Gamma^{A_\mu^a A_\nu^b}(p) = -i \delta^{ab} (g_{\mu \nu} p^2 - p_\mu p_\nu + \frac{1}{\zeta}n^\mu n^\nu) $$ and I am looking to solve for the inverse of ...
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Deriving gluon propagator in axial gauge

I am currently checking my work against an answer and I understand most of it except I am having difficulty understanding the signs in a particular part. The question is as follows: (a) Derive the ...
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Bibliography for the Quantization of the free electromagnetic field with the Lorenz gauge

Recently I have been studying QFT and when I arrived at the Gauge theory I learned that one can quantize the electromagnetic field with the Coulomb gauge and the Lorenz gauge. Regarding the Coulomb, I ...
4 votes
0 answers
214 views

Justifying the transverse-traceless gauge

For weak gravitational fields, we can assume the metric is some perturbation of flat space: $g_{ab} = \eta_{ab} + h_{ab}$. Following Schutz's argument, you can incorporate a small coordinate ...
Kiwi breeder's user avatar
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Possible mistake at Nakahara: $F_{\mu\nu}$ vanishing for a particular $A_\mu$

In equation $(1.293)$ of Nakahara's Geometry, Topology and Physics, he says that the Yang-Mills field tensor $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu+g[A_\mu,A_\nu]$ for a gauge field $$A_\mu=...
AFG's user avatar
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4 votes
0 answers
86 views

What is meant by Coulomb gauge not being Lorenz invariant? [duplicate]

This question is in the context of QFT. The notes says: A disadvantage of working in Coulomb gauge is that it breaks Lorentz invariance. What is meant by Coulomb gauge not being Lorenz invariant? The ...
Jochem4T's user avatar
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0 answers
32 views

Is any choice of electric and vector potentials valid, as long as the correct gauge transformation exists?

For example, in general one would not choose a gauge with $\phi \neq 0$ and $\vec{A}=0$ because that simply gives you the electrostatic case where $\vec{B}=0$. However one can transform this into $\...
agaminon's user avatar
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3 votes
0 answers
122 views

Find smooth gauge numerically in the presence of symmetries

Let's assume a gapped two-band model in $2$D characterized by a Bloch-Hamiltonian $h(k_x,k_y)$ in the presence of reflection symmetry along the $x$ direction represented on the orbital degrees of ...
zltn.guba's user avatar
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13 votes
2 answers
2k views

Trouble reconciling these two views on gauge theory

Very generally speaking, I view gauge theory as asking what local symmetries leave our theory invariant and then seeing the consequences. Thus, taking a look at the Lagrangian for electromagnetism, we ...
CBBAM's user avatar
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3 votes
3 answers
235 views

When we solve the Maxwell equations for $(\phi,{\bf A})$ in a gauge, will the solution $(\phi,{\bf A})$ automatically obey the gauge condition?

As the title of the question suggest; how you could determine if a gauge fixing is a condition or a requirement. Let me explain. Imagine you are working with Maxwell's Equations. By the definition of ...
Álvaro Rodrigo's user avatar
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64 views

2D Quantum Hamonic oscillator in magnetic field with a shiftted position

Background Consider a hole in a 2D parabolic potential in a magnetic field which is generate by the following gauge: $$ \vec{A} = \left( - \frac{B_z y}{2}, \frac{B_z x}{2},0\right) $$ Our quantum ...
Shankar Das Sarby's user avatar
1 vote
0 answers
69 views

Faddeev-Popov Method for Gauge Fixing in CFT (Light-ray Operators)

I was attempting to go through the paper by Petr Kravchuk and David Simmons-Duffin: https://arxiv.org/abs/1805.00098 where I encountered the following Just below E.4, it is mentioned that for the ...
Sahil Saha's user avatar
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0 answers
68 views

Is there an error in this Wikipedia article: "Landau quantization"?

I am trying to do a homework, so I had to consult this Wikipedia article Landau Quantization where it is mentioned that for the symmetric gauge $\vec{\textbf{A}} = \frac{1}{2}(-\textbf{B}y, \textbf{B}...
Mahammad Yusifov's user avatar
1 vote
0 answers
83 views

Gauge Fixing in Derivation of Lorentzian OPE Inversion Formula in 2D CFT

I have been looking through the following article: https://arxiv.org/abs/1711.03816 and wish to understand the derivation from scratch. The definition of conformal partial waves and the object of ...
Sahil Saha's user avatar
1 vote
1 answer
96 views

Why does $\mathbf{A}(x) = \frac{1}{2}(\mathbf{B}(x) \times \mathbf{x})$ work?

In my textbook, the identity for a possible vector potential $$\mathbf{A}(x) = \frac{1}{2}(\mathbf{B}(x) \times \mathbf{x})$$ is used. How is this valid? If I compute the curl, I get $$\mathbf{B}(x) \...
EE18's user avatar
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0 answers
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How to get retarded scalar potential in Coulomb electrodynamics and what's the use?

In Coulomb gauge electrodynamics with potential $(\phi,\vec{A})$ and source $(\rho,\vec{J})$ we obtain the Poisson's equation for the scalar equation and the wave equation with transverse current ...
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4 votes
1 answer
130 views

Why is $Z_3= Z_\xi$ in a non-abelian gauge theory?

In my lecture notes for a course on QFT it is said that, also in non-abelian gauge theories, the identity $Z_3 = Z_\xi$ holds, where those renormalization parameters belong respectively to the ...
Albert's user avatar
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0 answers
27 views

Choosing the Gauge in Randall–Sundrum model

Given the $5D$ conformally flat metric in Randall–Sundrum model $ds^2=e^{-2A(y)}\eta_{MN}dx^Mdx^N$, where $x^5=y$ The Einstein tensor is given by $G_{MN}=\frac{1}{2M^3}(\Lambda g_{MN}+T_{\mu\nu}\delta^...
neutrino's user avatar
3 votes
2 answers
573 views

Quantum Theory of Radiation Enrico Fermi 1932

I was reading Fermi's review on Dirac's "Quantum Theory of Radiation", which he published in 1932. I was unable to know why he expressed electric field as the following: I understand that ...
Jyotishraj Thoudam's user avatar
4 votes
2 answers
208 views

Propagator and Ward identity in the $R_\xi$ gauge

The full gauge propagator in the $R_\xi$ gauge is $$D_{\mu\nu} = \frac{i}{k^2+i\epsilon}\left(-g_{\mu\nu}+\frac{1-\xi}{k^2}k_\mu k_\nu\right).\tag{1}$$ Now if we take $\xi=0$, we get the Lorenz gauge, ...
Mohamed Ahmed's user avatar
3 votes
0 answers
76 views

Why is there always a $TT$-gauge coordinate system comoving with a test particle?

In section 35.5 of Gravitation by Misner, Thorne & Wheeler, when discussing the action of a gravitational wave on two test particles A and B, there is this statement: My question is why, to the ...
Sgia's user avatar
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2 votes
1 answer
186 views

Gauge-fixing condition invariant under auxiliary gauge transformation

In quantum gravity one usually splits the metric $g= \bar{g}+h$ into a background field $\bar{g}$ and a fluctuation field $h$. In order to obtain a propagator one has to gauge fix the action (e.g. ...
Silas's user avatar
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3 votes
1 answer
237 views

Temporal Gauge with periodic boundary conditions

In Yang-Mills theory with periodic boundary conditions in time, is the temporale gauge, i.e. $A_0 = 0$, well defined? Periodic boundary conditions would be $$A_\mu(T_2,x) = A_\mu(T_1,x).$$ Naively I ...
Fra's user avatar
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2 votes
1 answer
111 views

Invariance of gauge-fixing condition in background field method

In the Peskin & Schröder (chapter 16.6) they use the background field method and spilt the gauge field into an background field $A$ and a fluctuation field $\mathcal{A}$. Next they claim that the ...
Silas's user avatar
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5 votes
0 answers
103 views

Validity of Lorenz gauge in non-Abelian gauge theory

I understand that this is a long shot, especially because it's such a niche question but: has it been mathematically proven that (under sufficient smoothness conditions, etc.) any field configuration ...
Sam Blitz's user avatar
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4 votes
1 answer
170 views

Where is the Yennie gauge useful in Gupta-Bleuer formalism (or QED in general)?

Consider the Lagrangian of the Gupta-Bleuer formalism given by: $$\mathcal{L} =-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} -\frac{1}{2\xi}(\partial A)^2.$$ I understand the necessity of the gauge fixing term: ...
Samuel Adrian Antz's user avatar
2 votes
0 answers
107 views

Proving that the path integral formulation of scalar QED theory is independent of the choice of the gauge-fixing parameter $\xi$

I am considering the following scalar QED lagrangian: $$L = −\frac{1}{4}F_{\mu\nu}^2 + |D_{\mu\varphi}|^2 − m^2|\varphi|^2− \frac{1}{2\xi}(\partial_\mu A^\mu)^2.$$ Where I want to show that the ...
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0 answers
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Proving that the Faddeev-Popov path integral is independent of the gauge choice? [duplicate]

I know that the Faddeev-Popov path integral is gauge invariant. But how does one show that \begin{equation} I = \int \mathcal{D}\mathcal{A}_\mu \bigg|\frac{\delta\mathcal{G}}{\delta{\omega}}\bigg|\...
QFTheorist's user avatar
1 vote
1 answer
181 views

Gauge choice and observable quantities

Assume that I have the usual $U(1)$ gauge field $A_{\mu}$. We know that observable quantities are invariant under global transformations of the form $A_{\mu}\rightarrow A_{\mu}'=A_{\mu}+\partial_{\mu}\...
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