Philosophical considerations on the Aharonov-Bohm effect

Dipankar Home, S. Sengupta

The controversy concerning theoretical treatment of the Aharonov–Bohm (AB) effect is critically investigated. A new approach, taking the time-dependent aspect of this effect into consideration, is proposed which seeks to resolve the prevalent ambiguities. This provides interesting insight into the origin of the AB effect. Some clarifications are also made regarding the experimental verification of this effect.

Murray Peshkin

Líu, Jùn

We study a generalization of Aharonov-Bohm effect, the potential effect. The discussion is focused on field-free effects in simply connected region, which obviously can not have any local field-flux. Among the published discussions about this kind of effects, it is generally agreed that this kind of effects does not exist due to gauge invariance. However, there are also opinions that this effect is a trivial variation of Aharonov-Bohm effect and therefore there is no need to check its existence. To my knowledge, it has never been tested. My first goal here is to supply enough theoretical reason to motivate the experimental test of this effect. I start with an intuitive derivation, then I introduce a wave-front theory as a theoretical consideration. Logically, the existence of potential effect implies the existence of the AB effect, but not vice versa. The purpose of this paper is to provide a physical connection in the opposite direction.

Benjamin Liebowitz

Miguel Rodriguez

Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-Bohm effect which involves a coherent superposition of particles with opposite charges moving along a single open interferometric path. By means of the experimental considerations a limit $\sqrt{\ensuremath{\theta}}\ensuremath{\simeq}{\left(0.13\phantom{\rule{0.16em}{0ex}}\text{T}\text{eV}\right)}^{\ensuremath{-}1}$ is achieved, improving by 10 orders of magnitude the results derived by Chaichian et al. [Phys. Lett. B 527, 149 (2002)] for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.

G N Afanasiev