On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane

TL;DR

This paper develops a gauge-invariant minimal coupling prescription for a charged spinless particle in a noncommutative plane with a magnetic field, clarifying previous naive approaches and exploring the gauge structure via Seiberg-Witten maps.

Contribution

It introduces a consistent, gauge-invariant minimal coupling method for noncommutative quantum mechanics and analyzes the associated gauge structure using Seiberg-Witten maps.

Findings

Established a gauge-invariant minimal prescription

Explicitly computed Seiberg-Witten maps for the system

Clarified differences from naive minimal coupling approaches

Abstract

In this paper, we provide a mathematically and physically consistent minimal prescription for a charged spinless point particle coupled to a constant magnetic field in a 2-dimensional noncommutative plane. It turns out to be a gauge invariant prescription in contrast to the widely and carelessly used naive minimal prescription in the context of 2-dimensional quantum mechanics in a noncommutative plane. Besides, we explore the noncommutative U(1) gauge theoretic structure of the underlying noncommutative system by explicitly computing the 1-parameter family of Seiberg-Witten maps.