Bose description of the generalized Pauli spin operators and para super symmetry

Abstract

In this paper, the generalized fermion algebra is introduced so as to have the [Formula: see text]-dimensional Fock space. The generalized Pauli spin matrices of order [Formula: see text] are introduced by identifying these matrices with the step operators of the generalized fermion algebra. From the [Formula: see text]-graded parity relation [Formula: see text] generalized Pauli matrices are obtained. Finally, the para super symmetry (SUSY) is realized in terms of these matrices and ordinary bosonic operators.