Minimal Bosonization of Supersymmetry with Zp-graded Parity

Abstract

In this paper we consider the Z p -graded parity generalizing the ordinary (or Z 2 -graded ) parity. Using the Z p -graded parity operator, we discuss the minimal bosonization of the N=2 SUSY with Z p -graded parity. The lowest energy level is shown to be infinitely degenerate. In order to avoid the infinite degeneracy of the ground state we introduce the paraboson algebra to obtain the para-supersymmetry. Finally, we discuss the hidden SUSY with Z 3 -graded parity.