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

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SUMMARY

The geometry of the gauge potential in the Aharonov-Bohm (A-B) experiment is characterized as topologically a hemisphere inside the solenoid and a truncated cone outside. This conclusion is supported by the foundational work of T. T. Wu and C. N. Yang in their 1975 paper, "Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields," published in Physical Review D. The article by Bernstein and Phillips from 1981 on fiber bundles and quantum fields serves as a valuable reference for understanding these geometric properties.

PREREQUISITES
  • Understanding of gauge theory and its applications in quantum mechanics.
  • Familiarity with fiber bundles and their role in modern physics.
  • Knowledge of the Aharonov-Bohm effect and its implications.
  • Basic grasp of topology, particularly in relation to geometric structures.
NEXT STEPS
  • Read T. T. Wu and C. N. Yang's paper on gauge fields for in-depth insights.
  • Explore Bernstein and Phillips' article on fiber bundles for foundational concepts.
  • Investigate the mathematical framework of fiber bundles in quantum field theory.
  • Study the implications of the Aharonov-Bohm effect in various physical contexts.
USEFUL FOR

Physicists, particularly those specializing in quantum mechanics and gauge theory, as well as students and researchers interested in the geometric aspects of quantum fields and the Aharonov-Bohm effect.

Anko
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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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