The topological AC effect on noncommutative phase space

TL;DR

This paper investigates the Aharonov-Casher effect within noncommutative quantum mechanics, employing a generalized Bopp's shift method to derive phase corrections on noncommutative space and phase space.

Contribution

It introduces a novel application of Bopp's shift method to analyze the AC effect in noncommutative settings, avoiding the star product approach.

Findings

Derived corrections to the AC phase on NC space.

Derived corrections to the AC phase on NC phase space.

Provided a new method for solving Dirac equations in noncommutative frameworks.

Abstract

The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on noncommutative space and noncommutative phase space by the new method, we obtain the corrections to AC phase on NC space and NC phase space respectively.