Pauli equation on noncommutative plane and the Seiberg-Witten map

TL;DR

This paper explores the noncommutative Pauli equation in two dimensions, utilizing the Seiberg-Witten map to relate it to a commutative problem, and derives the energy spectrum including all orders of noncommutativity parameter .

Contribution

It introduces a method to incorporate the Seiberg-Witten map into the noncommutative Pauli equation and derives the  corrected energy spectrum.

Findings

Energy spectrum is corrected by  in  noncommutative plane.

Seiberg-Witten map effectively relates noncommutative and commutative problems.

Supersymmetry is exhibited at gyro-magnetic ratio 2.

Abstract

We study the Pauli equation in noncommutative two dimensional plane which exhibits the supersymmetry algebra when the gyro-magnetic ratio is $2$. The significance of the Seiberg-Witten map in this context is discussed and its effect in the problem is incorporated to all orders in $\theta$. We map the noncommutative problem to an equivalent commutative problem by using a set of generalised Bopp-shift transformations containing a scaling parameter. The energy spectrum of the noncommutative Pauli Hamiltonian is obtained and found to be $\theta$ corrected which is valid to all orders in $\theta$.