Para-Fermi algebras and the many-electron correlation problem.

A new formulation of the many-electron correlation problem is presented based on the use of parastatistics. It is shown that second-order para-Fermi creation and annihilation operators, which correspond to the creation and annihilation of spin-averaged paraparticles, occur naturally for the spin-independent many-electron problem. Moreover, the spin-independent many-electron Hamiltonian is directly expressible in terms of the parafield operators. The structure of the general paraFermi algebra is also investigated from the viewpoint of the pseudo-orthogonal group O(2n +1, 1). Finally, an exphcit matrix representation for the para-Fermi algebra of order 2, which enables one to handle even particle-number-nonconserving operators, is obtained in a canonical U(n)-adapted basis.