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

Using para-Grassmann, or generalized Grassmann algebras, we define rat ional power of annihilation and creation operators, in order to extend supersymmetric quantum mechanics. This extension can be replaced, und er some assumptions, in para-Grassmann quantum mechanics. We then appl y 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 do ne by means of a Hamiltonian defined as a sum of 2s monomials of degre e 2s + 1.