A What is the geometry of a gauge potential in the A-B experiment?

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The discussion centers on the geometry of the magnetic vector potential in the Aharonov-Bohm (A-B) experiment, referencing an article by Bernstein and Phillips from 1981. The authors assert that the geometry is topologically a hemisphere inside the solenoid and a truncated cone outside it. A key reference for understanding the geometry and topology related to the A-B effect is the work by Wu and Yang, which discusses nonintegrable phase factors. The conversation also includes a request for a link to the original article for further reading. Understanding these geometrical aspects is crucial for grasping the implications of gauge potentials in quantum fields.
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Aharonov-Bohm effect
Hi, this is a question about an article in the Scientific American magazine.

In 1981 Bernstein and Phillips wrote an article about fiber bundles and quantum fields, and I believe it's still a useful reference, the kind of thing lecturers would use at university.

Anyway, my question is, how do the authors determine that the geometry of the magnetic vector potential, in the original A-B experiment, is topologically a hemisphere, and that outside the solenoid the potential is geometrically a truncated cone?
 
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Do you have a link to the article? Concerning the geometry/topology and the AB effect a standard reference is

T. T. Wu and C. N. Yang, Concept of nonintegrable phase factors and global for-
mulation of gauge fields, Phys. Rev. D 12, 3845 (1975),
http://link.aps.org/abstract/PRD/v12/i12/p3845
 

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