Yesterday, Sir Michael Berry gave a talk at the Institute of Physics of UNAM, about the Ahoronov Bohm effect. The effect consists in an observable phase change in the wave-function of electrons that travel along magnetic field free regions of space, due to a magnetic flux in a region unaccessible to the electrons. Thus, it seems that there is a non-local interaction with the magnetic field, which seems unacceptable. or a local interaction with the vector potential, which is also unacceptable due to the non-uniqueness of the gauge.
The Ahoronov-Bohm effect was predicted by Ehrenberg and Siday in 1948 using an argument based on the Dirac's phase exp(i\int d\vec l\cdot\vec A) around the flux line. The argument was not exact, as it did not take into account that an electron can turn many times around the shielded magnetic flux, and it yielded a non-single-valued result. Ahoronv and Bohm rediscovered the effect in 1959 finding an exact solution for the quantum mechanical problem of an electron moving in a multiply connected space pierced by a magnetic flux. Dr. Berry showed us that the exact single valued result may be obtained as a Poisson topological sum of whirling waves, each of whose terms corresponds to a given number of turns around the flux and is not si9ngle valued, but the sum is indeed single valued.
Chambers in the 60's provided experimental verification of the effect, but it rouse certain controversy. Was the effect due to the return fields? to the switching electric fields? The controversies seem to have been solved now.
There are actually four A-B efects, as the wave and the flux could each be quantum or classical. For example, ripples scattered by a vortex in a fluid is a classical-classical instance of the A-B effect. Another analogy is a simple interferometer.
There is a close connection between the A-B effect and scattering by a semi-infinite half-wave plane. This is made explicit by using the edge gauge. in which the vector potential is different from zero only in a half plane that ends at the flux line. Thus, the tools of optics, i.e., Fresnel diffraction integrals, may be used to study the effect.
He mentioned an application to quantum chaos in billiards, in which a flux line would break down time reversal symmetry but would leave the classical trajectories unchanged. This has been discussed with Thomas Seligman.
Finally, he mentioned that the physically relevant field is not the magnetic field, nor the vector potential, nor the line integral of the vector potential but its imaginary exponential.
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