# 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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### Integral of gauge field bulk to boundary propagator in AdS

I'm studying from the book "Introduction to the AdS/CFT Correspondance" by Horatiu Nastase. In page 190, he defines the gauge field bulk-to-boundary propagator in Euclidean $AdS_{d+1}$ given ...
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### Why does the Lorenz gauge condition impose a relationship between $\vec A$ and $V$?

background I read in the book Introduction to Electrodynamics by D. J, Griffiths the process of solving the four Maxwell equations in the most general form: Firstly, the four equations were simplified ...
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I want to know that does $F^{a}[A_{\mu}] = 0$ condition used in Faddeev-Popov Quantization has unique solution $A_{\mu}$ or is it $F^{a}[A^{\theta}_{\mu}] = 0$ should have unique $\theta$ as solution ...
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### Transverse traceless gauge in linearized GR

I'm reading about gravitational waves and I'm wondering how we know we can always go to the transverse and traceless gauge? Going to the de Donder gauge is fine, I can follow that, but then showing ...
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### Hamiltonian for charge particle in electromagnetic field in dipole approximation

Why can the Hamiltonian $$H = \frac{1}{2m}\left(\vec{p}-q\vec{A}\right)^2+q\Phi + V$$ be transformed to $$H = \frac{1}{2m}\vec{p}^2 - q \vec r \vec E + V$$ in the dipole approximation, in which ...
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### Is special relativity falsified by the Aharonov Bohm effect?

The Lorenz gauge is the only Lorentz invariant electrodynamic gauge. If the vector potential has physical meaning, as in the Aharonov–Bohm effect, then the gauge condition can not be arbitrarily ...
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### Singularities in gauge-fixing conditions and topological defects

I am studying the 't Hooft's paper "Topology-of-the-gauge-condition-and-new-confinement" https://doi.org/10.1016/0550-3213(81)90442-9 and there are several points which I would like to ...
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### Examples of Chern number calculations where more than two $U(1)$ gauge of wavefunction has been used

While computing the Chern number of electronic wave functions \begin{align} \left|\psi\right\rangle = \begin{pmatrix}\cos\left(\frac{\theta}{2}\right) \\ \sin\left(\frac{\theta}{2}\right)e^{i \phi} \...
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### How does the gauge-fixing term break gauge invariance?

Given the gauge-fixing term $\mathcal{L}_\mathrm{gf}=-\frac{1}{2\xi}(\partial_\mu A^\mu)^2$ and the gauge transformation $A_\mu\mapsto A_\mu+\partial_\mu\alpha$, how does the term break gauge ...
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In the classroom my teacher stated that the Gauge-fixing term in the action $$\frac{1}{2\alpha}\int d^4x (\partial_\mu A^\mu(x))^2$$ transforms under $A_\mu(x) \rightarrow A_\mu(x)+\partial_\mu \... 1answer 45 views ###$R_\xi$gauges and the EM-field$R_\xi$-gauges are said to be a generalization of the Lorenz gauge. I dont quite get why we add the term $$\mathcal L_{GF} = - \frac{(\partial_\mu A ^\mu)^2}{2\xi}$$ to the Lagrangian. If i ... 2answers 101 views ### Gauge invariance for classical fields I recently did some exercises in classical field theory and tried to think deeply about the gauge symmetry of the free electromagnetic field described by the Lagrangian $$\mathcal L = -\frac 1 4 F^{\... 0answers 47 views ### Gauge invariance and the degrees of freedom [duplicate] I am currently starting to learn some QFT. And I am very confused by the fact that the freedom to choose a gauge for a theory controls the physical degrees of freedom. Please correct me if i am wrong ... 1answer 40 views ### What are all the gauge symmetries & derivatives of the QED lagrangian? I find that the gauge symmetries of the lagrangian are a topic that gets obfuscated quite a bit. I'm trying to understand the big picture of this in QED. My understanding is that: Gauge derives its ... 0answers 23 views ### Relation between polarization vector sums and propagators and the use of ghosts It is commonly argued that, according to the BRST treatment, ghosts cannot appear as initial or final states, and that the only states that can be used as initial or final states are physical gauge ... 0answers 32 views ### What are the main issues with gauge theories of gravity? [duplicate] From what I understand, the obvious problems with a gravity being a posed as a gauge theory of the Lorentz group are the residual tetrad fields having no obvious gauge theoretic interpretation, as ... 1answer 90 views ### Where does the Goldstone couplings go in the unitary gauge? Imagine that you have some model with an enlarged scalar potential, such that there is, for instance, a quartic coupling \kappa between the Higgs charged component and three other scalars, which do ... 0answers 25 views ### Difference in the Lagrangian when working with different gauges like, I have a Standard model Lagrangian, then what will be the differences in interaction terms and in interaction vertices if we work with the Feynman gauge and unitary gauge? 0answers 44 views ### Understanding the gauge condition in light-cone gauge When going over Cambridge String Theory Notes (page 38) I came across the following gauge conditions:$$X^+ (t, \sigma) = x^+(t)\hspace{5mm}, \hspace{5mm} P_−(t, \sigma) = p_−(t) \tag{1} $$which is ... 0answers 41 views ### Lagrangian density for a free EM field I wanted to derive the Lagrangian density of a free EM field \mathcal{L} in the Lorenz gauge as:$$ \mathcal{L} =- \frac{1}{4} F_{\mu \nu} F^{\mu \nu} = \frac{1}{2} A_{\mu} \partial^2 (g^{\mu \nu}- ... 1answer 78 views ### For the free electromagnetic field, is it possible make single gauge transformation to achieve$\phi={\bf \nabla}\cdot{\bf A}=0$? For any electromagnetic field, it is easy to impose the Coulomb gauge condition${\bf\nabla}\cdot{\bf A}=0$. To start with, if${\bf \nabla}\cdot{\bf A}_{\rm old}\neq 0$, the trick is to make a gauge ... 0answers 32 views ### Why retardation showed up for Lorentz gauge but not coulomb gauge? There's two common gauge used for EM, Lorentz gauge and Coulomb gauge However, if you look at the solution of those gauge, the retardation only showed up for Lorentz gauge, but not for coulomb gauge. ... 1answer 48 views ### Consistency condition for Yang-Mills on a Torus So I was recently studying 't Hooft's paper on self-dual solutions to Yang-Mills on$\mathbb{T}^4$. So the basic idea is that you consider a box with periodic boundary conditions and then you impose ... 0answers 50 views ### Is Lagrange multiplier an arbitrary gauge? A related post might be found here: Is the gauge transform field in electromagnetism a Lagrange multiplier? Consider the case of Lagrange multiplier$L=f(x)+\lambda g(x)$where$g(x)=0$was a ... 1answer 85 views ### Path integral formulation of an Abelian Field Theory, unclear identity TL;DR: How exactly does one come to this identity $$\int\mathcal{D}G(A^\alpha)\delta(G(A^\alpha)) = \int\mathcal{D}\alpha(x)\delta(G(A^\alpha)) \mathrm{det}\left(\frac{\delta G(A^\alpha)}{\delta\... 1answer 100 views ### Landau levels in rotationally invariant gauge I try to find wave-function of electron in external constant magnetic field in gauge$$A=\frac{B}{2}(-y,x,0).$$I substitute anzats, \psi=e^{-i\omega t}e^{ip_zz}F(x,y). Then, I rewrite equation in ... 1answer 50 views ### Coulomb gauge in magnetostatics should give divergence-free vector potential Say we're dealing with magnetostatics (\vec{\nabla} \cdot \vec{j} = 0 ). If we define \vec{A} to satisfy \vec{B} = \vec{\nabla} \times \vec{A}, and we take the assumption that \vec{\nabla} \... 4answers 208 views ### What does adding a gauge fixing term -\frac{1}{2\xi}(\partial_\mu A^\mu)^2 really mean? Given any electric and magnetic field (or F_{\mu\nu}), there is always some freedom in defining what A_\mu(x) should be. In fact, there are infinite choices for A_\mu(x). This is because for an ... 0answers 48 views ### Independence of S-matrix in QED of the gauge choice The Feynman rules in QED often use different expressions for the free photon propagator (e.g. Feynman gauge, Landau gauge, and others). Is there a textbook on the subject which explicitly checks ... 1answer 44 views ### Gauge transformations of potentials with a step function In have a question about the following exercise. I am given the following expressions for the scalar and vector potential,$$\vec{A}(\vec{r},t) = \frac{\sigma}{\epsilon_0}\left[\frac{x}{c}\hat{x} + tU(... 1answer 86 views ### When one says that Yang Mills theory is a non-abelian field theory, what specific gauges and gauge transformations are implied in this statement? What specific gauges and gauge transformations are implied when one states that the order of such gauge groups are vital? Can this please be explained as simple as possible (: 0answers 147 views ### Gauge transformation issues of Proca Lagrangian It seems to be trivial to claim that the mass term in Proca Lagrangian is NOT "gauge invariant". The claim show up in Wikipedia or section 6.3 in Greiner's book "Field Quantization". But I'm puzzled ... 0answers 52 views ### Is comoving coordinate a gauge choice? Consider the Roberston Walker metric in 4D, $$ds^2 = -dt^2 + a^2(t) \left( \frac{dr^2}{1-kr^2} +r^2 d\Omega^2_2 \right)$$ Now, if we consider the collapse of a spherically symmetric fluid, spherically ... 0answers 27 views ### What is the way to express Yang-Mills symmetry groups without gauges? Given a Yang-Mills theory such as$SU(3)$which has 8 gluons. After we gauge-fix this theory, it no longer has$SU(3)$guage symmetry. Yet, we still use the group constants and the 8 types of gluons ... 1answer 182 views ### How to show the that Lorenz gauge is true given that the scalar and the magnetic vector potentials are not unique? So I understand that we select the divergence of A (magnetic vector potential) to be: $$\frac{1}{c^2}\dot{\phi} + \nabla\cdot\vec{A} = 0.$$ The Lorenz gauge (1). because of the symmetries in ... 1answer 205 views ### Why is the gauge-fixing condition squared in the QED Lagrangian? Consider the free Maxwell Lagrangian: $$L= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}.$$ As we know, the gauge symmetry$A_{\mu} \rightarrow A_{\mu}+\partial_\mu \lambda\$ must be fixed when quantizing the ...
I have a question on the quantization of the gauge theory with minimal coupling term. What I understand is that if one is given an action $$S=-\int d^4 x \frac{1}{4}F^2 \tag1$$ Since this action has ...