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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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 ...
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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?
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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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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 ...
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98 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, ...
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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{...
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573 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?
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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 ...
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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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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 ...
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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- ...
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49 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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53 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=\...
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72 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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37 views

Gauge invariance of quantum scalar field coupled to classical electromagnetic potential

I would like to quantize a scalar field that is coupled to a classical electromagnetic field $A_\mu$. More precisely, I start with the action (signature -+++) $$ S=\int d^4x\left(-|(\partial_\mu+iqA_\...
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76 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} \...
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114 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 ...
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47 views

Is Feynmann gauge reduce always physical gauge?

Is Feynmann gauge reduce always physical gauge? I heard in QCD, Feynmann gauge does not always give correct physics. The lecture says, "Fenymann gauge gives physical gauge, if the theory contains ...
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191 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 ...
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55 views

Different Signs in Yang Mills Gauge Transformations

I have seen the Yang-Mills Gauge Theory be constructed in many books and papers, however I have seen pretty much equal disparage of + and minus signs in the following equations, the definition of the ...
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69 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 + \...
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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 ...
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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}{\...
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171 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\...
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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 (...
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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 ...
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102 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): $$ (\...
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244 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 ...
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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 ...
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95 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\...
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144 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 ...
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108 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 ...
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38 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?
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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":...
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60 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}{\...
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176 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 ...
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159 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}\...
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94 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: Determine the Electric field using ...
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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 ...
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146 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 ...
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165 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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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_{\...
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303 views

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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282 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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85 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 ...
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164 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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294 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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96 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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86 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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222 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 ...