Supersymmetry in the Non-Commutative Plane

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.