The Noncommutative Anandan's Quantum Phase

TL;DR

This paper investigates the effects of noncommutative geometry on the quantum phases of a neutral particle with dipole moments, deriving noncommutative versions of known geometric phases and effects.

Contribution

It introduces a noncommutative framework for analyzing the Anandan's quantum phase and related effects, extending previous models to include noncommutative phase space.

Findings

Derived the noncommutative Anandan's geometric phase.

Obtained the noncommutative version of the He-McKellar-Wilkens effect.

Showed that the phase is a geometric dispersive phase in noncommutative space.

Abstract

In this work we study the noncommutative nonrelativistic quantum dynamics of a neutral particle, that possesses permanent magnetic and electric dipole momenta, in the presence of an electric and magnetic fields. We use the Foldy-Wouthuysen transformation of the Dirac spinor with a non-minimal coupling to obtain the nonrelativistic limit. In this limit, we will study the noncommutative quantum dynamics and obtain the noncommutative Anandan's geometric phase. We analyze the situation where magnetic dipole moment of the particle is zero and we obtain the noncommutative version of the He-McKellar-Wilkens effect. We demonstrate that this phase in the noncommutative case is a geometric dispersive phase. We also investigate this geometric phase considering the noncommutativity in the phase space and the Anandan's phase is obtained.