The role of the electromagnetic potentials in quantum mechanics. The marton experiment

Abstract

New arguments against the existence of the magnetic Aharonov-Bohm effect are given. In particular, the following points are emphasized: i) the time evolution of the expectation value of any observable depends only on the forces, and not on the potentials; ii) the choice of a Stokesian or a non-Stokesian vector potential is quite irrelevant; iii) if Bohm’s ideas were right, one could prove the existence of an Aharonov-Bohm effect also for aclassical charged continuum; iv) the recent analysis of the Marton experiment, due to Greenberger and Overhauser, proves that this experiment has nothing to do with the Aharonov-Bohm effect. Finally, in appendix A, the nonexistence of the electric Aharonov-Bohm effect is also proved. In appendix B, a nonrelativistic treatment of quantum electrodynamics, due to Pauli, which avoids completely the electromagnetic potentials, is briefly recalled.