Normal ordering and a Wick-like reduction theorem for fermions with respect to a multi-determinantal reference state

We introduce the notion of normal ordering and Wick-like expansion of a product of fermionic creation/annihilation operators with respect to a multi-determinantal reference state psi(0). The new normal ordered products possess the following desirable properties: (a) their expectation values with respect to psi(0) vanish, and (b) the normal product of N operators does not depend in a special way on N. The analogues of contractions, unlike in the case of a single determinant reference function, can have n creation and n annihilation operators with n greater than or equal to 1. We prove a Wick-like reordering theorem for a product of creation/annihilation operators, which generates a sum of products in the new normal ordering with any number of contractions. The formula can be generalized to cover products of normal ordered products of operators as well. (C) 1997 Published by Elsevier Science B.V.