Aharonov - Bohm Effect.

[Mojo jojo]

I am now studying the Aharonov - Bohm effect, and I am very puzzled about it.

Does this effect suggest non locality of the magnetic field?

If not, does it suggest that vector potential is a physical entity?

If it does, then how do I reconcile gauge invariance with the identity axiom?

[stephen_speicher]

I am now studying the Aharonov - Bohm effect, and I am very puzzled about it.

Does this effect suggest non locality of the magnetic field?

If not, does it suggest that vector potential is a physical entity?

If it does, then how do I reconcile gauge invariance with the identity axiom?

These are exactly the issues that Aharonov and Bohm were concerned about in their classic paper on the effect some forty-five years ago. Although I doubt the paper itself will provide you with any new insights, it is worth reading for perpsective and historical note. The reference is Y. Aharonov and D. Bohm, "Significance of Electromagnetic Potentials in the Quantum Theory," Physical Review, Vol. 115, No. 3, pp. 485-491, August 1, 1959. If you do not have ready access to these journals, the paper is also reprinted in an excellent resource of classic papers in the development of modern gauge theory. The book is Gauge Theories in the Twentieth Century, John C. Taylor, Editor, Imperial College Press, 2001.

In the original paper the perspective of the authors is that the electromagnetic potentials are in fact more fundamental than the fields. As gauge theory developed and locality was more formally dispensed with, the particle-field interaction was taken to be nonlocal and the potential itself had a mathematical reality as the integral of the potential over all paths. Most physicists today take the Aharonov-Bohm effect to arise from quantum mechanics and take the effect itself to be a confirmation of the standard theory.

One might think that, with due consideration of special relativity, that if the physical system relied on the potential in the field-free multiply-connected space, that one might consider that something real was there. But no local theory could account for the phenomena and integrate with classical electromagnetism where the vector potential is considered just a mathematical artifact. Hence, the standard theory and nonlocality. But now such a theory does exist, and you can read the paper here.

[Alan Forrester]

I am now studying the Aharonov - Bohm effect, and I am very puzzled about it.

Does this effect suggest non locality of the magnetic field?

If not, does it suggest that vector potential is a physical entity?

If it does, then how do I reconcile gauge invariance with the identity axiom?

The gauge is just a description that is useful under some circumstances. The observations that supposedly prove that the Aharonov Bohm Effect exists can all be explained in terms of the electromagentic field without bothering with the vector potential. The AB paper makes idealisations that don't work in real life, like an infinitely long solenoid and the approximation that the charged particle's wave function doesn't penetrate the solenoid when in fact it does. Michael Berry has some papers that explain it here:

http://www.phy.bris.ac.uk/research/theory/...blications.html

Edited August 14, 2005 by Alan Forrester