(p,q)-Sheaves and the Representability Problem

General properties of new models of the electronic Fock spaces based on the notion of (p, q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by κ-electron means (κ = 2, 3,. . .) is described and studied in detail for the case of sheaves induced by κ-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in κ-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach.