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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Lapse and shift in ADM decomposition

Poisson in Relativist's Toolkit and also other authors in various papers state explicitly that after one does the 3+1 decomposition, the lapse and shift $N$ and $N^a$ are non-dynamical variables, and ...
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775 views

Wess-Zumino Gauge in non-Abelian supersymmetric theory

I've got a question concerning non-Abelian supersymmetric gauge theories. Consider supersymmetric non-Abelian theory realized on chiral superfields $\Phi_i$ in a representation $R$ with matrix ...
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122 views

How is this a gauge choice mathematically?

I've been reading an article about the "square cat", which is described as the system bellow Such system is a deformable body that can change $a$ and $\theta$ but has $b$ fixed. The article uses this ...
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420 views

Local phase gauge in momentum space of Bloch state

We know Bloch state has a phase undetermined, so $\Psi_k \to \Psi_k' = e^{i\theta(k)}\Psi_k$ is still the same eigenstate. My question: Are there some restriction on $\theta(k)$ except to be a real ...
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1answer
469 views

Free electromagnetic field in Lorenz gauge

To get rid of the extra term in the QED Lagrangian we need to redefine the electromagnetic four-vector: $A^{\mu} \rightarrow A^{\mu} - \frac{1}{c} \partial_{\mu} a(x)$ where $a(x)$ is the function ...
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162 views

Eigenvalue of Hamiltonian under gauge transform of Bloch state

$H = \sum_{k} V(q) a_{k4}^{\dagger}b_{k3}^{\dagger}b_{k2}a_{k1}$ where $q$ is the transfer momentum, $a$ $b$ are two orbits or two sublattice sites. Will the eigenvalues of the above Hamiltonian ...
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107 views

Properties of Fluids-theoritical confusion

I am having a very basic confusion on how we calculate the height of atmosphere when we assume that the density does not change with altitude(density remains 1.29 kg/m$^3$). I want to know why we say ...
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427 views

Why Lagrangian of electromagnetism with Lorenz Gauge evolve Klein Gordon equation?

Simply Lagrangian without a source for Maxwell equation is $$ L = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} $$ Also Lorenz Gauge condition is $$ \partial_{\mu}A^{\mu}=0 $$ and if so I can briefly add this ...
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Why the extra term $\frac{1}{2}(\partial_{\rho}A^{\rho})^2$ in the photon Lagrangian?

In my quantum field theory class we have been told to use this Lagrangian for the photon field $$\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta} -\frac{1}{2}(\partial_{\rho}A^{\rho})^2.$$ but ...
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What is a gauge in a gauge theory?

As I study Jackson, I am getting really confused with some of its key definitions. Here is what I am getting confused at. When we substituted the electric field and magnetic field in terms of the ...
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Landau level degeneracy in symmetry gauge, finite system

As we know, Landau level degeneracy in a finite rectangular system is $\Phi/\Phi_0$, where $\Phi=BS$ is the total magnetic flux and $\Phi_0=h/q$ is the flux quanta. This can be easily derived using ...
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538 views

Why should it be allowed to set the einbein to unity?

The Polyakov action for a massive free point particle with worldline $\gamma$ is given by $$ S[\gamma] = \frac{1}{2}\int_\gamma e \biggl(\frac{1}{e^2}\dot{x}^2 - m^2\biggr)\mathrm{d}\tau $$ where $e$...
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What is conformal gauge?

I often see in physics articles on gravity such notion as conformal gauge and Weyl transformation. They use Conformal gauge to change coordinates to transform metrics from arbitrary $$ds^2=g_{\mu \...
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Hamiltonian for Electron in Magnetic Field with Symmetric Gauge in Polar Coordinates

I am new on the board and have a question about how to write the Hamiltonian for an electron in a magnetic field rotating at a fixed radius. I would like to write the hamiltonian using the symmetric ...
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634 views

Vector bosons: polar vectors or axial vectors?

The $W$ and $Z$ bosons are known as vector bosons, because they have non-zero spin. How do we know whether they are axial or polar vectors? Context: I am reading about a technique called Operator ...
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Clarifications needed on Gauge Fixing and Ghosts [closed]

The first time some kind of gauge fixing appears is during the Gupta-Bleuler procedure, which is used to be able to quantize the photon field: The basic gauge invariant Lagrangian leads to $\Pi_0=0$ ...
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Connection between Gauge Fixing Term and Gauge Condition [duplicate]

In Peskin on page 514, when deriving the Faddeev-Poppov ghosts, they arrive at the full Lagrangian for Yang-Mills: $$ \mathcal{L} = -\frac{1}{4}F^2 + \frac{1}{2\xi} (\partial \cdot A^a)^2+\textrm{...
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138 views

Ambiguous points in spontaneous symmetry breaking of discrete symmetry

For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we don'...
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826 views

General relativity: gauge fixing

In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, ...
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338 views

Why does reparameterisation invariance lead to gauge-fixing?

In Becker, Becker and Schwarz, the point particle action is given in terms of an auxiliary field $e(\tau)$ as: \begin{align} \tilde{S}_0 = \frac{1}{2}\int \,d\tau \left(e^{-1}\dot{X}^2 - m^2e\right) \...
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Showing that Coulomb and Lorenz Gauges are indeed valid Gauge Transformations?

I'm working my way through Griffith's Introduction to Electrodynamics. In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and electric ...
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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?

Edit: Use this PO.org question instead. Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, ...
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929 views

Faddeev-Popov Gauge-Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
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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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174 views

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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997 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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174 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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74 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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421 views

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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261 views

Unitary gauge for non-abelian case

I'm reading Chapter 19 of Mandle and Shaw's Quantum field theory. In the first section it is explained that one can go with a $SU(2)$ followed by a $U(1)$ transformation from $$\begin{bmatrix}\eta_1(x)...
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1answer
671 views

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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2answers
496 views

Gauge-fixing of an arbitrary field: off-shell & on-shell degrees of freedom

How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
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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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146 views

$E$ and $B$ fields in Axial Gauge

I am trying to compute the $\vec{E}$ and $\vec{B}$ fields in the Axial gauge ($n \cdot \vec{A}=0$) where $n^2=1$, but I'm having trouble seeing the usefulness/how it simplifies the equations.
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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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1answer
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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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1answer
453 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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1answer
301 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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Physical difference between 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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1answer
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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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1answer
424 views

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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604 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
533 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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3answers
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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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2answers
770 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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1answer
259 views

The Lorenz gauge in electrodynamics

What is the fundamental reason to fix the Lorenz gauge to $0$?
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580 views

What is non-Abelian about non-Abelian Chern-Simons' theory?

One is aware that in the axial gauge (say the light-cone gauge $A_{-}=0$) non-supersymmetric Chern-Simons' theory is a quadratic theory. Hence in this gauge there are no gauge-gauge interactions. Then ...