A unified view on Aharanov-Bohm like phases and some applications

Abstract

The analysis of the Aharanov-Bohm phase and other similar physical effects in this paper is motivated by the philosophy that all physical changes, including phase changes, should originate in one of the local physical interactions even if they are described elegantly and concisely as topological or geometric changes. The topological or geometric nature comes about either due to an additional physical principle or due to certain special spatial or temporal property of the fields from the source. Similar remarks apply to rotation or precession of polarization and spin vectors. As a primary example I describe the Aharanov-Bohm phase as arising from the Coulomb interaction of a charge in the electrostatic potential created by other charges. The topological nature comes about because the interaction energy has zero gradient throughout space, except in a compact region enclosed by the quantum paths. This analysis brings out the unifying aspects of the scalar and the vector A-B effects, and the Aharanov-Casher phase. Then I discuss two other related problems with descriptions in the geometrical and the interaction pictures; I discuss how quantum complementarity is realized without the Heisenberg back action on momentum in certain atom interferometry experiments. In the second example, I show that the Thomas precession of the spin results from the local torque in the accelero-magnetic field, a field predicted in analogy with the gravitomagnetic field. I end the discussion with some remarks on the classical nature of fringe shifts in Aharanov-Bohm like phenomena in electromagnetism and gravitation.