Para-Grassmann algebras with applications to para-Fermi systems
Yoshio Ohnuki, S. Kamefuchi · Journal of Mathematical Physics · 1980
Grassmann algebras of the usual kind are generalized to what are to be called para-Grassmann algebras. Para-Grassmann numbers are defined as those satisfying the trilinear commutation relations that resemble the para-Fermi commutation relations. Basic mathematical properties of these algebras are studied in detail on the basis of generalized Grassmann algebras discussed in the preceding paper. Applications are made to description of para-Fermi systems, and it is found that such systems can completely be described in what we call the para-Grassmann representation.