Irreducible representations of Z22-graded N=2 supersymmetry algebra and Z22-graded supermechanics

Abstract

Irreducible representations (irreps) of Z22-graded supersymmetry algebra of N=2 are obtained by the method of induced representation, and they are used to derive Z22-graded supersymmetric classical actions. The irreps are four-dimensional for λ = 0, where λ is an eigenvalue of the Casimir element, and eight-dimensional for λ ≠ 0. The eight-dimensional irreps reduce to four-dimensional ones only when λ and an eigenvalue of Hamiltonian satisfy a particular relation. The reduced four-dimensional irreps are used to define Z22-graded supersymmetry transformations, and two types of classical actions invariant under the transformations are presented. It is shown that one of the Noether charges vanishes if all the variables of specific Z22-degree are auxiliary.