Noncommutative Geometry and Geometric Phases

TL;DR

This paper explores particle dynamics in noncommutative phase space, revealing effects analogous to magnetic fields and Berry curvature, and examines the Aharonov-Bohm effect within this framework.

Contribution

It introduces a generalized noncommutative phase space model incorporating monopole-like and Berry curvature effects, analyzing their impact on quantum phenomena.

Findings

Noncommutative phase space simulates effective magnetic fields.

Aharonov-Bohm effect analyzed with noncommutative operators.

Physical implications of noncommutative structures discussed.

Abstract

We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space. The Ahranov-Bohm effect has been considered in this form of phase space, with operatorial structures of noncommutativity. Physical significance of our results are also discussed.