The inadmissibility of non-Stokesian vector potentials in quantum mechanics. Comments on a paper asserting the nonexistence of the Aharonov-Bohm effect

Abstract

Since the publication of the first paper of •HARONOV and BOHM (1) in 1959, discussion has concentrated mainly on questions of interpretation with regard to the role of the electromagnetic potentials in quantum mechanics (2). Doubts as to the reali ty of the effect itself have so far only been raised in private communications and answered by A~A~ONOV and BoH~ in one of their follow-on papers (3). In a recently published article (4) of BOCCHIERI and LOING]~R, however, the nonexistence of one of the effects predicted by AI~ARO~OV and BoH~--namely that related to the vector potent ia l -has been asserted. Because the experimental situation is not so convincing that any objection to the conclusions of ArIARONOV and BOgM can be rejected out of hand, we have undertaken a critical examination of this article. BOCCHI~RI and LOINGER consider a rotating charged particle the trajectory of which is in field-free space and contains an area within which a magnetic field is present. As the whole problem consists in clarifying which vector potentials are admissible in a description of the AharonovBohm (AB) experiment, the question as to whether the eigenvalues of the particle are influenced by the magnetic field is in fact equivalent to the question of the existence of the AB effect. The gauge invariance of the second kind is also valid in the case of a magnetic field vanishing throughout space. I t then means that the general representation of momentum operators and wave functions assumes the form