All Questions
Tagged with gauge-theory electromagnetism
353
questions
4
votes
1
answer
70
views
Can we impose Coulomb gauge without using temporal gauge in source-free Maxwell electrodynamics?
Coulomb gauge is $$\vec{\nabla} \cdot A=0$$ Now, from expression for electric field in terms of potentials $\vec{E}=-\vec{\nabla} \phi-\frac{\partial \vec{A}}{\partial t}$ and Gauss Law $\vec{\nabla} \...
- 43
2
votes
1
answer
133
views
Is the bundle of the Aharonov-Bohm effect like the tangent bundle of a cylinder or like the tangent bundle of a truncated cone?
Both are trivial bundles, and the natural (metric) connection is flat (curvature-free) for both. The difference between them is that the holonomy of the tangent bundle of the cylinder is trivial while ...
- 745
0
votes
0
answers
79
views
Quantizing the electric field without quantizing vector potential
I am trying to quantize the electromagnetic field, without using the vector potential. I start with a Fourier expansion:
$$\begin{equation}
\vec{E}(\vec{r},t) = \sum_{\epsilon} \vec{\epsilon} \int \...
- 1,258
0
votes
2
answers
73
views
Gauge transformation with harmonic one-form
The electromagnetic four-potential $A^{\mu}$ is not uniquely determined by the physical situation. We have the equation $$\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu}=F^{\mu\nu}.$$
Here $F^{\nu\mu}$ is ...
- 1,440
1
vote
0
answers
44
views
Wick rotation of Electromagnetic Field Lagrangian [duplicate]
So i will directly to the problem. I am not getting how, when we Wick rotate, the EM action should go to (the correct answer)
$$ S_E = \int -d^4 x\frac{1}{4} F_{\mu \nu} F^{\mu \nu} \underbrace{\...
- 980
1
vote
1
answer
147
views
How particles interact with the electromagnetic potential $A^\mu$?
It is well known that one reason quantum mechanics started to being developed, was because scientist wanted a model to explain electron orbits in atoms.
Borh interpreted that the for orbits to exist ...
- 1,515
0
votes
0
answers
60
views
Degree of freedom - Lorentz transfomation reduces it? [duplicate]
I am having a real difficult to counting degree of freedom. In fact, I notice that sometimes I am confused about what exactly we count as DoF, and what we do not count.
See, for example, the ...
- 980
1
vote
0
answers
48
views
Gauge redundancy and Gauge fixing
Take any gauge invariant theory, for instance QED. The QED Lagrangian is invariant under
$$A_{\mu}(x)\rightarrow A'_{\mu}(x)=A_{\mu}(x)+\partial_{\mu}. \alpha(x)$$
I have chosen a local gauge ...
- 3,982
0
votes
0
answers
111
views
Are eigenvalues of slashed covariant derivative real?
I am trying to demonstrate that the slashed covariant derivative
$$
\gamma^\mu D_\mu = \gamma^\mu(\partial_\mu -iA_\mu)
$$
has real eigenvalues:
$$
\gamma^\mu D_\mu \varphi_m(x)=\lambda_m \varphi_m(x)...
- 161
2
votes
4
answers
124
views
For these gauge transformations in electromagnetism, $\phi\to \phi-\partial_t \lambda$ and $\vec A\to \vec A+\nabla\lambda$, why do the signs differ?
I was looking at this question on Mathematics S.E, as I would like to know the origin of the signs in the gauge transformations of the scalar and vector potentials components, $\phi$ and $\vec A$, of ...
- 61
1
vote
1
answer
75
views
Magnetic vector potential in 1+1 spacetime dimensions
In the theory of electromagnetism in 1+1 spacetime dimensions (one temporal and one spatial coordinate), one can define the 2-potential vector (analogous to the 4-potential vector in 3+1 spacetime ...
0
votes
1
answer
99
views
Can we express the electrodynamic potentials $V$, $\mathbf{A}$ in terms of the electrodynamic fields $\mathbf{E}$, $\mathbf{B}$?
In Griffiths' Introduction to Electrodynamics problem 10.25, I am asked to draw a "triangle diagram" illustrating the relationship between (1) the sources $\rho$, $\mathbf{J}$, (2) the ...
- 660
0
votes
0
answers
47
views
Can the derivative of a gauge-invariant quantity be gauge-dependent?
I am wondering whether it is possible for derivatives of a gauge-invariant quantity to be gauge-dependent. Certainly, the converse is true; taking the curl of a gauge-dependent quantity (the vector ...
- 327
1
vote
0
answers
50
views
Bibliography for the Quantization of the free electromagnetic field with the Lorenz gauge
Recently I have been studying QFT and when I arrived at the Gauge theory I learned that one can quantize the electromagnetic field with the Coulomb gauge and the Lorenz gauge.
Regarding the Coulomb, I ...
0
votes
0
answers
69
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Action for scalar field with externally specified EM fields and gauge
Consider the following Lagrangian for a complex scalar field $\Psi$ along with an electromagnetic environment,
$$\mathcal{L} = ([\partial_\mu - i e A_\mu] \Psi)^* [\partial^\mu - i e A^\mu]\Psi - V(\...
