The Noncommutative Anandan's Quantum Phase

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.

15 pages, revtex4, version to appear in Physical Review A

References in corpus (3)

• The topological AC effect on noncommutative phase space
• Quantum Mechanics on Noncommutative Spacetime
• Noncommutative Geometry and Geometric Phases

Cited by in corpus (6)

• Landau quantization for a neutral particle in presence of topological defects
• Geometric Phase for Neutral Particle in the Presence of a Topological Defect
• Gravitational Geometric Phase in the Presence of Torsion
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• On atomic analogue of Landau quantization
• Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates