Clifford algebra and unitary group formulations of the many-electron problem

Abstract

An essential role of Clifford algebras for quantum-chemical finite-dimensional orbital models of many-electron systems is pointed out. The relationship between Clifford algebra matric units, the generators of the unitary group approach (UGA) and the higher order replacement or excitation operators, as well as between their first and second quantized realizations, is elucidated. The usefulness of higher order replacement operators in the spin-adaptation of various many-body theories is briefly outlined and illustrated on the orthogonally spin-adapted coupled-pair approach. A natural connection with the Clifford algebra UGA is explored and new possibilities for its exploitation in large scale configuration interaction calculations are suggested.