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dewitt claimed in his paper

Bryce S. DeWitt. Quantum theory without electromagnetic potentials, Phys. Rev. 125 no. 6 (1962), pp. 2189-2191, DOI: 10.1103/PhysRev.125.2189,

that the discovery of the Aharonov and Bohm that electromagnetic potentials play primary role in quantum mechanical theory is false. Who won? What are the errors in the argument of the losing side in this battle?

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What is the full reference to DeWitt's paper? –  Qmechanic Aug 27 '12 at 23:15
    
I added the reference to DeWitt's paper in question. –  Newman Aug 27 '12 at 23:22
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I think reading these two follow-up papers by Aharonov and Bohm will clarify the issue: prola.aps.org/abstract/PR/v125/i6/p2192_1 and prola.aps.org/abstract/PR/v130/i4/p1625_1 . –  Heidar Aug 27 '12 at 23:30
    
Thank you Heidar, I will read these two. –  Newman Aug 27 '12 at 23:36
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1 Answer

There is no losing side in this battle--- DeWitt is pointing out that you can express the local vector potential in a nonlocal form in terms of the fields everywhere in space. If you know E and B everywhere, you can figure out what A is supposed to be, once you choose a gauge. This is not in contradiction to the statement that the local equations of motion involve only A.

The reason nobody tries to do this anymore is because in nonabelian theories, as in electromagnetism on nontrivial topologies, you can't reconstruct A nonlocally from E and B, you need to know the Wilson loops.

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