The HMW effect in Noncommutative Quantum Mechanics

TL;DR

This paper investigates the He-McKellar-Wilkens (HMW) effect within non-commutative quantum mechanics by solving Dirac equations on NC space and phase space, revealing explicit additional terms due to non-commutativity.

Contribution

It provides explicit solutions and topological phases of the HMW effect in non-commutative spaces, extending understanding of quantum effects in non-commutative geometry.

Findings

Derived topological HMW phase on NC space

Identified additional terms from space-space non-commutativity

Identified additional terms from momentum-momentum non-commutativity

Abstract

The HMW effect in non-commutative quantum mechanics is studied. By solving the Dirac equations on non-commutative (NC) space and non-commutative phase space, we obtain topological HMW phase on NC space and NC phase space respectively, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.