Affiliation:
1. Department of Physical Science, Osaka Prefecture University, Nakamozu Campus, Sakai, Osaka 599-8531, Japan
Abstract
Irreducible representations (irreps) of [Formula: see text]-graded supersymmetry algebra of [Formula: see text] are obtained by the method of induced representation, and they are used to derive [Formula: see text]-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 [Formula: see text]-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 [Formula: see text]-degree are auxiliary.
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
3 articles.
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