Realisations of the representations of para-Fermi algebra in Fock space of Bose operators: part I

Abstract

Using the matrix realisations of para-Fermi operators we find isomorphic mappings with respect to the Green product of the para-Fermi algebra into second-order polynomials of creation and annihilation para-Bose operators with arbitrary order of parastatistics. In the Fock space ℋ 2 1 of two Bose operators all the irreducible representations of the para-Fermi algebra are realised. The spaces ofn-particle Bose statesn=1,2,..., from which ℋ 2 1 is constructed as a direct sum, can be interpreted as spaces of para-Fermi states of para-statisticsn.