Space Structure for the Simplest Parasupersymmetric System

Abstract

Structure of the state-vector space for a system consisting of one mode parabose and one mode parafermi degree of freedom with the same parastatistics order $p$ is studied and a complete, orthonormal set of basis vectors in this space is constructed. There is an intrinsic double degeneracy for state vectors with $m$ parabosons and $n$ parafermions, where $m\ne 0$, $n\ne 0$, and $n\ne p$. It is also shown that the degeneracy plays a key role in realization of exact supersymmetry for such a system.