The Aharonov-Casher and scalar Aharonov-Bohm topological effects

TL;DR

This paper revisits the topological and nonlocal properties of the Aharonov-Casher and scalar Aharonov-Bohm effects, clarifying their gauge structures and correcting previous misconceptions based on an incorrect Hamiltonian.

Contribution

It explicitly demonstrates the U(1) gauge structure of these effects and corrects prior arguments by analyzing and refuting an incorrect Hamiltonian used in earlier work.

Findings

Confirmed the topological nature of the effects

Clarified the gauge structure involved

Refuted previous incorrect arguments

Abstract

We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying U(1) gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyse the arguments of M. Peshkin and H. J. Lipkin (Phys. Rev. Lett. 74, 2847(1995)) in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect.