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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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9
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2answers
757 views

Why is $p_y$ conserved in the Landau gauge when we know the electron moves in circles?

Considering the cyclotron in $xy$-plane where the magnetic field is $\vec{B}=(0,0,B)^{T}$. In the Landau gauge, we have $\vec{A}=(0,Bx,0)^T$ and we obtain the Hamiltonian $$H=\frac{\hat{p}_x^2}{2m}+\...
2
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1answer
82 views

Electron photon interaction - commutation of $\mathbf{A}$ and $\mathbf{p}$

I'm trying to figure out the radiative transition rates between electronic levels due to EM radiation using FGR as done by Merzbacher, this online source, and others. I have two questions regarding ...
3
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0answers
159 views

Gauge invariance in General relativity and Classical Electrodynamics

As I understand from popular talks that gauge invariance is a problem in finding out exact solutions of Einstein's field equations (apart from the complication that it is non-linear), and gauge fixing ...
7
votes
2answers
196 views

Coordinate conditions in black hole solutions

The most general metric for a static and spherically symmetric metric is given by: $$ ds^2 = e^{2\gamma(u)}dt^2 - e^{2\alpha(u)}du^2 - e^{2\beta(u)}d\Omega^2 $$ I have the freedom of choosing ...
4
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0answers
832 views

Why not use the Weyl gauge?

In E&M in Minkowski space, the Lorenz and Coulomb gauges are typically used since they make things vastly simpler. On a curved background, Maxwell's equations (without sources) can be written as: ...
2
votes
1answer
452 views

Gauge invariance in QED

I could never understand the choice of gauge in QED. Let's say I know that $A_{\mu}$ has 4 components, hence 4 degrees of freedom. For, say, a photon I need only two. Let's say I pick Lorentz gauge ...
7
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2answers
382 views

Schwinger-Dyson equations in the Coulomb gauge

Introduction As far as I know (and please correct me if something is wrong!) the usual narrative to deal with perturbation theory in QED with the Coulomb gauge goes as follows: First, the gauge ...
1
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1answer
397 views

Light-cone coordinates to quantize strings?

Zweibach, in A First Course in String Theory said: "We now discuss a coordinate system that will be extremely useful in our study of string theory, the light-cone coordinate system", then he mentioned ...
4
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1answer
83 views

Choosing a solenoidal vector potential in gauge fixing

When finding a potential vector for the $\vec{B}$ field I understand that we have certain freedom because if $\nabla \times \vec{A}=\vec{B}$ then $\vec{A'} = \vec{A} + \nabla \psi$ also satisfies $\...
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0answers
27 views

Coherence of gauge fixing with the corresponding theoretical gauge freedom

I understand that for a gauge fixing to be valid, it needs to be achievable (i.e., become an identity) continuously through a sequence of allowed gauge transformations of the canonical variables, yet ...
6
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2answers
6k views

What is the physical meaning of Lorenz gauge condition? [closed]

What is the physical meaning of Lorenz gauge condition? And what part of the solutions we throw?
2
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1answer
348 views

Gauge invariance of non-Abelian theories under Pauli-Villars-Regularisation

Under the ordinary Pauli -Villars Regularisation one introduces a heavy mass ($\Lambda$) term $$\frac{1}{p^2-m^2+i\epsilon} \rightarrow \frac{1}{p^2-m^2+i\epsilon} - \frac{1}{p^2-\Lambda^2+i\epsilon}....
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0answers
79 views

Validity of gauge fixing in classical electrodynamics [duplicate]

I am working through Griffith, and was confused by some of the restrictions he imposed on the potentials in introducing the Coulomb and Lorenz gauge. It is easy to see that adding some arbitrary ...
3
votes
1answer
159 views

Geometrical point of view of the harmonic constraints ($\Delta g_{ij}=0$) in General Relativity

What does it mean, from the geometrical point of view, use (in General Relativity) of the constraints on the metric tensor's coefficients such that $\Delta g_{ij}=0$? (where $\Delta$ is the Beltrami-...
0
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1answer
129 views

Is $A_\mu A^\mu=0$ a good gauge fixing? [closed]

I am taking a course in classical electrodynamics and I am facing this problem Prove that $A_\mu A^\mu=0$ is a good gauge fixing or not. If it is, there are residual gauge freedom? I know that, ...
2
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0answers
84 views

Unitarity Gauge : how to undo the gauge transformation

I will simplify the argument. Let's consider a Gauge Boson (like the gauged one of U(1), $A_\mu$). Then, consider the Higgs boson with exponential representation, then $$H = e^{i\pi(x)/v}\left(\begin{...
9
votes
3answers
840 views

Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
1
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1answer
63 views

Can an electromagnetic potential be in two gauges at once?

I have a plane wave vector potential found using the free field form of Maxwell's equations and the Lorentz gauge: $\vec{A}(\vec{r},t) = \vec{A}_0 e^{i(\vec{k}\cdot\vec{r}-\omega t)}$ If I take the ...
1
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0answers
282 views

Coulomb Gauge under Lorentz Boost

In the Coulomb gauge for the Maxwell potential we have $$ A^0 = 0 \\ \partial_i A^i = 0 $$ Under an infinitesimal Lorentz Transformation with parameter $\epsilon$, we have $$ A^\mu(x) \rightarrow ...
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0answers
135 views

Gauged supergravity

It is said that in N=2 supergravity coupled to vector multiplets and hypermultiplets, one can gauge the R-symmetry by equivalently gauging the isometries of the corresponding hyperkahler cone over the ...
3
votes
2answers
269 views

Why do different vector potentials in Landau levels problem lead to different quantum mechanical ground state wavefunctions?

Consider a charged particle (electron) moves in xy plane under a magnetic field pointing along the z direction, i.e., $\vec{B}=B\hat{z}$. As a consequence, we can write down three different gauges- ...
2
votes
1answer
255 views

What is the meaning of 'physical gauge'?

What does it mean for a gauge to be a physical gauge in your gauge choice of the theory, and why is it called the "physical gauge"?
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2answers
318 views

Uniqueness of the magnetic vector potential?

I am trying to find the magnetic vector potential a distance of $s$ (cylindrical radial variable) from an infinite wire carrying current $I$. The magnetic field at a distance $s$ from a wire is $$B=\...
1
vote
1answer
141 views

How do integral representations of $\mathbf A$ and $\Phi$ satisfy Lorenz condition?

The following are the integral solutions of the potentials, obtained from the retarded potentials (by a Fourier transform): $$\mathbf A (\mathbf r) = \frac{\mu_0}{4\pi}\int_V \frac{\mathbf J (\mathbf ...
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2answers
630 views

What does it mean to be unique in terms of vector potentials?

I was in an electromagnetism lecture, where we were looking at the magnetostatic Maxwell’s equations: $$\begin{align} \nabla\cdot\mathbf{B} &= 0 \\ \nabla\times\mathbf{B} &= \mu_0\mathbf{J} \...
0
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1answer
2k views

How to find gauge pressure in pipe

If I have a pipe for which I know the height and velocity of the fluid at the left and right end, and I am asked to find the gauge pressure at the right end, how would I go about doing this if the ...
0
votes
1answer
226 views

Is Feynman gauge reduce always physical gauge?

Is Feynman gauge reduce always physical gauge? I heard in QCD, Feynman gauge does not always give correct physics. The lecture says, "Feynman gauge gives physical gauge, if the theory contains ...
2
votes
1answer
211 views

Unbounded perturbed geometry due to analyticity

I have an interesting mystery for you, loosely inspired on work related with this question. I have a certain Ansatz for a gravitational wave perturbation of the metric $h_{\mu \nu}$ that is nonzero ...
2
votes
2answers
3k views

Magnetic vector potential of an infinite wire

Using the integral $$A=\frac{\mu_0}{4 \pi} \int \frac{I \vec{dl}}{r}$$ for calculating magnetic vector potential of an infinite wire we get $$A = \left(\frac{\mu_0 I}{4 \pi}\right) \ln(\sec \theta + \...
27
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0answers
2k views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
2
votes
3answers
3k views

Why can the divergence of vector potential be anything?

Purcell in his book was deriving the vector potential $\bf A$ using $\text{curl}\;(\text{curl}\; \mathbf A)= \mu_0 \mathbf J\; .$ After some algebra, he came to this: $$-\frac{\partial^2 A_x}{\...
2
votes
2answers
418 views

Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )

I'm trying to understand the way that the Higgs Mechanism is applied in the context of a $U(1)$ symmetry breaking scenario, meaning that I have a Higgs complex field $\phi=e^{i\xi}\frac{\left(\rho+v\...
2
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0answers
113 views

Lorenz Gauge Dipole Potentials Formulation In SI Units? [closed]

After hunting in vain* for a documented closed form solution (ie: no integrals or differentiation in the formula) for $\phi$ in terms of A under the Lorenz condition, of an electrically short dipole (...
2
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0answers
43 views

Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
1
vote
1answer
284 views

Modified gauge fixing condition in Faddeev-Popov approach

Which gauge fixing conditions are allowed to choose for this approach? For example (following the steps of Peskin in 9.4) I can choose a "modified" lorenz gauge ( for a abelian theory): $$ (\...
0
votes
1answer
1k views

How can I prove that the axial gauge is a valid Gauge fixing condition?

I am studying classical electrodynamics and I have been introduced to the concept of gauge transformations and gauge fixing conditions. Right know I am trying to prove that some conditions are valid ...
0
votes
0answers
166 views

Equal-time commutation relations, Feynman propagator for gauge parameter $\lambda = 1$, physical meaning

Classical electromagnetism (with no sources) follows from the actions$$S = \int d^4x\left(-{1\over4}F_{\mu\nu}F^{\mu\nu}\right),\text{ where }F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu.$$The ...
5
votes
1answer
183 views

Feynman propagator for arbitrary values of the gauge parameter $\zeta$

For the choice $\zeta = 1$ the Lagrangian can be brought into a particularly simple form upon integration by parts in the action integral. Equation$$\mathcal{L}' = -{1\over4}F_{\mu\nu}F^{\mu\nu} - {1\...
1
vote
1answer
592 views

Probability current for electron in uniform magnetic field: wave function forever splitting apart?

In this document http://hitoshi.berkeley.edu/221a/landau.pdf on Landau levels, in section 4, page 19, "Transitionally invariant Gauge", they analyze the free electron in a uniform magnetic field ...
1
vote
1answer
492 views

Number of states in a given Landau level

For an electron in a uniform magnetic field, in free space, we seek to find the number of allowed states in a given rectangle $L_x L_y$ (for some fixed Landau level). In effect we are tiling 2-D ...
0
votes
1answer
103 views

Is there any sense in which mesons could act as force carriers, in the way that gauge bosons do?

Gauge bosons are force carriers. Mesons are composite bosons and have similar characteristics to gauge bosons. Is there any sense in which mesons could act as force carriers?
1
vote
1answer
128 views

Gauge freedom in tetrad

I asked the question in the MathOverflow, but didn't get any response. I thought maybe better luck here. I'm reading the following paper about Petrov type D space times called "Type D vacuum metrics":...
0
votes
1answer
455 views

Determining the Lorenz gauge condition

I'm having a bit of trouble understanding how the gauge condition is found. Consider the potentials $V$ and $\vec A$ and $V'$ and $\vec A'$ so that $$\vec E = -\vec\nabla V -\frac{\partial\vec A}{\...
2
votes
1answer
527 views

Why is the electromagnetic four-potential $A_{\mu}$ not an observable?

Why within classical field-theory the electromagnetic four-potential (usually $A_{\mu}$) not an observable? In classical mechanics we don't have problems with energy measurements and in quantum ...
6
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2answers
605 views

Why can the Lorenz gauge condition always be fullfilled?

Why is the Lorenz gauge condition always possible for classical electromagnetic fields? So far I can only understand the following: If we perform a gauge transformation $A\mapsto A'=A+\mathrm{d}\...
1
vote
2answers
183 views

The notion of fixing a gauge

I don't understand the notion of gauge fixing; can we choose any gauge or are there some restrictions? For example why can we choose $\nabla\phi = 0$ here: https://physics.stackexchange.com/q/188778/...
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0answers
84 views

Does fixing a metric component have anything to do with diffeomorphism invariance?

It is well known that in general relativity, the metrics $g_{\mu \nu}$ and $g_{\mu \nu} + \epsilon L_\xi g_{\mu \nu}$ are physically equivalent, where $L_\xi g_{\mu \nu}$ is the Lie derivative of the ...
1
vote
2answers
484 views

Gauge transformation of Lagrangian

Suppose I have a Lagrangian density $\mathcal{L}(\phi^\mu,\sigma)$ depending on vector fields $\phi^\mu$ and their derivatives and a scalar field $\sigma$ and its derivatives. If I make a gauge ...
4
votes
1answer
388 views

Why do we have to choose a gauge to quantize a gauge theory?

Why do we have to choose a gauge to quantize a gauge theory? This was an exam question but I couldn't answer it.
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0answers
54 views

Vertex of gauge boson interaction in an arbitrary gauge

Let's have interaction between some gauge boson (for example, $W$ boson) and some other field, for example, let assume $\bar{u}\gamma_{\mu}(1 - \gamma_{5})d W^{\mu} + h.c.$. Let's then use gauge $R_{\...