Electronic Fock space as associative superalgebra

Abstract

New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches. Its study clarifies and simplifies the mathematical backgrounds of these approaches. And even more, it leads to many relations that would be very difficult to derive using conventional technique. Formulas for action of the creation-annihilation operators on products of state vectors are derived. Explicit expressions for action of simplest particle-conserving products of the creation-annihilation operators on powers of state vectors are given. General scheme of parametrization of representable density operators of arbitrary order is presented.