An Algebraic Approach to the Many-Electron Problem

Josef Paldus

M. D. Gould, Josef Paldus

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 para-Fermi algebra is also investigated from the viewpoint of the pseudo-orthogonal group O(2n+1, 1). Finally, an explicit 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.

Jacek Karwowski, Grzegorz Pestka

Huzio Nakano

The algebraic structure of the hamiltonian of the many electron system is studied. Based upon the second quantization scheme, a purely algebraic-theoretical method is established in order to determine the total energies of the many electron system, where each energy eigenstate of one electron in the Hartree-Fock field of these electrons is occupied by a given number of electrons. This occupation number is either 0, 1 or 2, because of the value, 1/2, of the electron spin. Only the part of the hamiltonian related to the singly-occupied states are found to be algebraically important, in relation to which the so-called exchange algebra emerges. We state the general principle how to manipulate this algebra, and will work out in some cases of a few numbers of singly occupied states. In the case that the energy eigenstates of the Hartree-Fock field have degeneracies, the theory so far mentioned does not suffice, and more detailed and somewhat complicated study is required.

Alexander Quandt

S. Fraga, Gulzari L. Malli, L. H. Thomas