The N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane

TL;DR

This paper constructs and solves an N=1 supersymmetric Landau problem, revealing a supersymmetric noncommutative superplane structure that extends the classical Moyal-Voros plane, with implications for supersymmetric quantum mechanics.

Contribution

It introduces a supersymmetric extension of the Landau problem and identifies the algebraic structure of the associated non(anti)commutative superplane.

Findings

Established the N=1 supersymmetric Landau problem.

Identified the algebraic structure of the supersymmetric superplane.

Extended the Moyal-Voros plane to a supersymmetric context.

Abstract

The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified.