MATRICIAL REPRESENTATION OF RATIONAL POWER OF OPERATORS AND PARA-GRASSMANN EXTENSION OF QUANTUM MECHANICS

Abstract

Using para-Grassmann, or generalized Grassmann algebras, we define rational power of annihilation and creation operators, in order to extend supersymmetric quantum mechanics. This extension can be replaced, under some assumptions, in para-Grassmann quantum mechanics. We then apply this method to the construction of an equation which generalizes the (2+1)D Pauli equation to a particle of arbitrary spin s. This is done by means of a Hamiltonian defined as a sum of 2s monomials of degree 2s+1.