Supersymmetry in the Non-Commutative Plane

TL;DR

This paper explores the supersymmetric extension of a non-commutative plane model, analyzing its symmetry charges and algebra, revealing a supersymmetric Galilei algebra with a central extension.

Contribution

It introduces a supersymmetric generalization of a non-commutative plane model and analyzes its algebraic structure using the Ostrogradski--Dirac formalism.

Findings

Determined Noether charges for the model's symmetries.

Found the Poisson algebra forms a supersymmetric Galilei algebra.

Identified a two-dimensional central extension in the algebra.

Abstract

The supersymmetric extension of a model introduced by Lukierski, Stichel and Zakrewski in the non-commutative plane is studied. The Noether charges associated to the symmetries are determined. Their Poisson algebra is investigated in the Ostrogradski--Dirac formalism for constrained Hamiltonian systems. It is shown to provide a supersymmetric generalization of the Galilei algebra with a two-dimensional central extension.