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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.

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.

446 questions
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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 explanation there is not very transparent, specially…
Alexander Cska
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21
votes
3 answers

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 scalar and vector potential in the inhomogeneous…
Roshan Shrestha
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20
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2 answers

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?
Moumita
  • 401
19
votes
1 answer

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. To "fix" this, we recognize that anyway we would…
PPR
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18
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1 answer

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 related by a gauge transformation are identified…
Prahar
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18
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2 answers

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 equations of motion for just the potentials $A^0$…
QuantumDot
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17
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2 answers

A question on gauge fixing

As I understand it, a physical theory that has a gauge symmetry is one that has redundant degrees of freedom in its description, and as such, is invariant under a continuous group of (in general) local transformations, so-called gauge…
Will
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13
votes
3 answers

Why is nonzero net charge density incompatible with the cosmological principle?

In an answer to a question about the overall charge-neutrality of the universe, benrg writes, A nonzero net charge density is incompatible with the cosmological principle. Unlike the gravitational field of a uniform mass distribution, which can be…
rob
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13
votes
2 answers

Trouble reconciling these two views on gauge theory

Very generally speaking, I view gauge theory as asking what local symmetries leave our theory invariant and then seeing the consequences. Thus, taking a look at the Lagrangian for electromagnetism, we can act on each point by a $U(1)$ action, i.e.…
CBBAM
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13
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3 answers

Are Maxwell's equations "physical"?

The canonical Maxwell's equations are derivable from the Lagrangian $${\cal L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} $$ by solving the Euler-Lagrange equations. However: The Lagrangian above is invariant under the gauge transformation $$A_\mu \to…
InertialObserver
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13
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3 answers

Can we do path integrals in gauge theories without fixing a gauge?

I am aware that when quantizing gauge theories with a path integral, one needs to add a gauge fixing term to avoid over-counting gauge related field configurations. From an aesthetic perspective, I find this procedure distasteful. I would like to…
Yossarian
  • 6,235
12
votes
4 answers

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 arbitrary function $\theta(x)$…
Solidification
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12
votes
2 answers

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…
Wein Eld
  • 3,791
12
votes
2 answers

What is the physical meaning of Lorenz gauge condition?

What is the physical meaning of Lorenz gauge condition? And what part of the solutions we throw?
grodta
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12
votes
2 answers

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 $$ds^2=g_{\mu \nu}dx^{\mu}dx^{\nu}$$ to…
xxxxx
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