Supersymmetric Quantum Mechanics on Non-Commutative Plane

TL;DR

This paper investigates supersymmetric quantum mechanics on a non-commutative plane, demonstrating the preservation of supersymmetry to all orders in the non-commutative parameter and deriving spectral corrections using the Seiberg-Witten map.

Contribution

It shows supersymmetry holds to all orders in non-commutativity for g=2 and derives first-order spectral corrections using Seiberg-Witten map.

Findings

Supersymmetry algebra holds to all orders in non-commutative parameter for g=2.

First-order correction to spectrum obtained via Seiberg-Witten map.

Eigenstates are unchanged if magnetic field is replaced by B(1+Bθ).

Abstract

We study the Pauli equation on non-commutative plane. It is shown that the Supersymmetry algebra holds to all orders in the non-commutative parameter $\theta$ in case the gyro-magnetic ratio $g$ is 2. Using Seiberg-Witten map, the first order in $\theta$ correction to the spectrum is obtained in the case of uniform magnetic field. We find that the eigenstates in the non-commutative case are identical to the commutative case provided the magnetic field $B$ is everywhere replaced by $B(1+B\theta)$.