Supersymmetry, parastatistics, and operator realizations of a Lie algebra

Abstract

The algebraic structure of parastatistics has been generalized and it is found to be consistent with supersymmetric quantum mechanics with supercharges constructed out of the generalized para-Bose and para-Fermi operators. It is further shown that the operator algebra of generalized parastatistics offers a realization of the (graded) orthosymplectic group similar to that of orthogonal and symplectic groups using conventional parastatistics.