Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates

TL;DR

This paper explores how noncommutative spatial coordinates influence the quantum phases of particles with dipole moments, deriving bounds on noncommutativity parameters from experimental phase data.

Contribution

It develops a formalism for quantum phases in noncommutative coordinates and applies it to key physical phenomena like Aharonov-Bohm and Aharonov-Casher effects.

Findings

Derived bounds for noncommutativity parameter theta from experimental phase data.

Generalized quantum phase formalism to noncommutative space.

Applied formalism to multiple quantum phase phenomena.

Abstract

The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms of a semiclassical constrained Hamiltonian system. The relation between the quantum phase acquired by a particle interacting with an electromagnetic field and the (semi)classical force acting on the system is examined and generalized to establish a formulation of the quantum phases in noncommutative coordinates. The general formalism is applied to physical systems yielding the Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and Anandan phases in noncommutative coordinates. Bounds for the noncommutativity parameter theta are derived comparing the deformed phases with the experimental data on the Aharonov-Bohm and Aharonov-Casher phases.