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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Energy Tensor, covariant derivate, variation respect to the metric [duplicate]

I'm doing the variation of a Lagrangian respect to the metric, but I am having problem with a particular terminus. My action is: $$ S=\int d^4x \sqrt{-g}[ (\nabla_\mu A^\mu)^2]$$ My lagrangian is: ...
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Is a lightlike vector potential (A²=0) a valid and/or useful choice?

I know most common choices to fix the gauge of a vector potential, but I wonder if there are no other choices possible. As a concrete example inspired by the Schrödinger equation with magnetic field, ...
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History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, but could you explain the history? It's ...
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Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics

How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that involves the ...
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Vector potential and gauge in electromagnetism

In a paper by Zimmerman [JOURNAL OF APPLIED PHYSICS 114, 044907 (2013)], it is stated that the Lorenz gauge in electromagnetism is the only gauge with real physical meaning. How do I reconcile this ...
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113 views

Equivalency of Gauge Conditions

How is the Lorenz gauge condition $\partial_\mu \overline{h}^{\mu \nu}=0$ equivalent to the harmonic gauge condition $\Box x^\mu=0 $?
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64 views

How to find solutions to the gravitational potential metric h

I'm working on a problem in which a star of mass M1, radius R1 is surrounded by a thin shell of mass M2, , radius R2. I want to find the solutions to the gravitational potential h in the region in ...
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45 views

Is it possible to incorporate the Lorenz gauge term into the electromagnetic fields?

I noticed that the Lorenz gauge term is represented by partial derivatives acting on the four-potential. Is it possible that the Lorenz gauge term could somehow be a similar object that belongs to the ...
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What is the physical consequence of the Lorenz Gauge Term not equaling zero?

What happens to the physics of the electromagnetic field if the Lorenz gauge term does not equal to zero? \begin{align} \partial_{\mu}A^{\mu} \neq 0 \end{align}
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What is the constraint on the Gauge Potential in the Covariant Gauges?

One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. ...
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Scalar potential in em field task

(Sorry for my English) Task. There is a volume with some arbitrary current or voltage source connected to wires. One wire is buried in the ground. I know values of electric and magnetic fields in ...
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Is the gauge fixing $\partial_\mu A^\mu + \gamma A_\mu A^\mu=0$ used in the literature and does it have a name?

In an exercise for a course on Gauge Theories, I was asked to derive the action of QED with the method by Faddeev and Popov, using the following gauge-fixing function: $$F(A) = \partial_\mu A^\mu + ...
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113 views

Symmetries of a Uniform Magnetic Field

Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel ...
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271 views

Gauge theory in classical electromagnetism

I understand gauge theory as the theory of continuous transformation group which keeps Lagrangian (or dynamics) invariant. So some integral invariants could be found. In terms of classical ...
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159 views

Coulomb gauge and two degrees of freedom of EM field

The EM field has two possible polarizations, which is caused by spin-one nature of field (leads to the Lorenz gauge) and massless of the field. Really, the Klein-Gordon equations for the EM field $$ ...
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147 views

EM vector potential

We can write the electromagnetic field tensor as $$\begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & 0 & ...
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Lorenz and Coulomb gauge-fixing conditions

Lorenz and Coulomb gauge-fixing conditions. What is physical difference between these two gauge-fixing conditions? Mathematical expression are clear but how to we choose one of these means what they ...
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529 views

Gauge fixing and degrees of freedom

Today, my friend (@Will) posed a very intriguing question - Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions ...
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Proof that we can always find a gauge transformation such that $A_0=0$?

I'm trying to follow Coleman's proof from his lectures "Aspects of Symmetry" on page 200-201. He proofs it is always possible to work in the temporal gauge for a general Yang-Mills-Higgs theory. I ...
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267 views

Can I call additional conditions on potentials a Gauge choice?

Let's say I have an electromagnetics problem in a spatially varying medium. After I impose Maxwell's equations, the Lorenz gauge choice, boundary conditions, and the Sommerfeld radiation condition, I ...
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How do I derive the Lorenz gauge from the continuity equation?

I was reading my old electromagnetics book (Elements of Electromagnetics, by Sadiku, 3rd edition) and after the author explained what the Lorenz gauge is mathematically and why it is useful in ...
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1answer
212 views

How to add a potential term to the Dirac Equation?

I've read that if you have a Hamiltonian for the Dirac Equation, you can add a potential term to it simply by adjusting the momentum operator so that $p^\mu \rightarrow p^\mu-A^\mu$, where $A^\mu$ is ...
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463 views

Showing Lorenz gauge is satisfied in retarded potential - vector calculus

I am trying to show that $\nabla\cdot \vec{A}=-\mu_0 \epsilon_0 \frac{\partial V}{\partial t}$ $V=\frac{1}{4\pi\epsilon_0}\int \frac{\rho(\vec{r}',t_r)}{r}d\tau'$ $\vec{A}=\frac{\mu_0}{4\pi}\int ...
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314 views

Lorenz gauge fixing

Is it always possible to define function $\psi$ satisfying the Lorenz gauge equation $$ \partial_{\mu}\partial^{\mu} \psi + \partial_{\mu}A^{\mu} = 0? $$
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167 views

The Lorenz gauge in electrodynamics

What is the fundamental reason to fix the Lorenz gauge to $0$?
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Intuition for gauge parallel transport (Wilson loops)

I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport". I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
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716 views

Gauge fixing choice for the gauge field $A_0$

In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole. Please can you provide me a ...
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115 views

Coupling of vector gauge and a massive tensor field

I was reviewing the paper-Coupling of a vector gauge field to a massive tensor field In the calculation I found the term $ 2\mu^2 \varepsilon^{ijk} \dfrac{\partial_j}{\partial^2}B_k\dot{B}$ which ...
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420 views

What is the difference between observer, frame of reference, and gauge?

It seems to me that there is considerable relationship between the three concepts: frame of reference, observer, and gauge. How do they overlap? My current understanding is that an observer with a ...
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Are gauge choices in electrodynamics really always possible?

If $B$ is magnetic field and $E$ electric Field, then $$B=\nabla\times A,$$ $$E= -\nabla V+\frac{\partial A}{\partial t}.$$ There is Gauge invariance for the trnasformation $$A'\rightarrow ...