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

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In summary, the conversation discusses an article written in 1981 by Bernstein and Phillips on fiber bundles and quantum fields. The article is still considered a useful reference and is often used by lecturers at universities. The question is about how the authors determine the geometry of the magnetic vector potential in the original A-B experiment, which is described as a hemisphere, and outside the solenoid, which is described as a truncated cone. The conversation also includes a link to another article by T. T. Wu and C. N. Yang, which is a standard reference for the geometry and topology of the AB effect. The link to the original article mentioned is also provided.
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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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1. What is a gauge potential in the A-B experiment?

A gauge potential in the A-B experiment refers to the vector potential, A, in the Maxwell's equations. It is a mathematical quantity that describes the electromagnetic field and its interactions with charged particles.

2. How is the gauge potential related to the geometry of the A-B experiment?

The gauge potential is related to the geometry of the A-B experiment through the electric and magnetic fields, which are determined by the curl and divergence of the gauge potential, respectively. The geometry of the experiment affects the values and directions of these fields, which in turn are determined by the gauge potential.

3. What is the significance of the gauge potential in the A-B experiment?

The gauge potential is significant because it allows us to mathematically describe and understand the behavior of electromagnetic fields in the A-B experiment. It helps us to predict and explain the interactions between charged particles and the fields, and has important applications in fields such as electronics and optics.

4. How is the gauge potential measured in the A-B experiment?

The gauge potential cannot be directly measured, but its effects can be observed and measured through the electric and magnetic fields. These fields can be measured using various instruments such as voltmeters and magnetometers, which can give us information about the gauge potential and the geometry of the experiment.

5. Can the gauge potential in the A-B experiment be changed?

Yes, the gauge potential can be changed by altering the geometry of the experiment or by introducing external electric or magnetic fields. This can have a direct impact on the behavior of the electromagnetic fields and the interactions with charged particles. However, the gauge potential itself is a mathematical quantity and cannot be physically manipulated.

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