All Questions
Tagged with aharonov-bohm gauge-theory
9
questions
2
votes
1
answer
135
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
7
votes
7
answers
2k
views
Is the magnetic vector potential "real" in classical electromagnetism?
From how I've learned it in school the magnetic vector potential is used as a mathematical tool to simplify problems with current-carrying wires in classical electromagnetism, but is never treated as ...
- 233
0
votes
1
answer
147
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Large gauge transformation in $\mathrm{U}(1)$ flux threading argument
In Oshikawa's flux threading argument for the $\mathrm{U}(1)\times T$ Lieb-Schultz-Mattis (LSM) theorem, the author defined a so-called large gauge transformation
$$U=\exp\left(i\frac{2\pi}{L}\sum_{\...
- 28
2
votes
1
answer
124
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How is the geometry of the magnetic vector potential determined in the original Aharonov-Bohm experiment?
I've tried but I can't find anything about the geometry of the gauge field, which is mentioned in an article in Scientific American 1981, by Bernstein and Phillips.
They say, without explaining it, ...
- 21
2
votes
1
answer
231
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Gauge choice in Aharonov-Bohm effect
In p.385 of Griffiths QM the vector potential $\textbf{A} = \frac{\Phi}{2\pi r}\hat{\phi}$ is chosen for the region outside a long solenoid. However, couldn't we also have chosen a vector potential ...
- 157
0
votes
1
answer
117
views
Phase term in Aharonov-Bohm effect
In $U(1)$ gauge, the transformation is given by $(c=1)$ $$e^{\frac{ie\int A_\mu dx_\mu}{\hbar}}$$ I know that this form comes from the phase picked up by electrons in Aharonov-Bohm effect. However, in ...
- 91
5
votes
1
answer
451
views
Deriving the non-abelian Aharonov-Bohm effect as a Berry phase
I am trying to derive the non-abelian Aharonov-Bohm effect by generalising Michael Berry's derivation to the case of non-abelian gauge field $A$.
My derivation so far
We require a degenerate ...
- 3,986
23
votes
2
answers
1k
views
What is the analog of the Aharonov-Bohm effect for general gauge fields and for gravity?
The Aharonov-Bohm effect concerns the electromagnetic fields, where a quantum particle can feel the effect of an electromagnetic field in regions where it vanishes, through the electromagnetic ...
- 7,720
24
votes
2
answers
3k
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What is the conclusion from Aharonov-Bohm Effect?
What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum ...
- 26.8k