Independent-cluster methods as mappings of quantum theory into classical mechanics

Summary The algebraic structures of theconfiguration interaction, normal coupled cluster, andextended coupled cluster methods are reviewed and developed. These methods are pointed out to perform a mapping of the quantum mechanical problem into a classical phase space, where in each case the classical canonical coordinates have characteristically different cluster and locality properties. Special focus is given to the extended coupled cluster method (ECCM), which alone is based on an entirely additively separable coordinate system. The general principles are formulated for systems with both bosonic and fermionic degrees of freedom, allowing both commutative and anticommutative (Grassmann) cluster amplitudes. The properties of the classical images are briefly discussed. It is proposed that phase spaces may exist which are fixed points of quantization.Based on a talk given at theWorkshop on Coupled-Cluster Theory at the Interface of Atomic Physics and Quantum Chemistry, Harvard-Smithsonian Institute for Theoretical Atomic and Molecular Physics, Cambridge, MA, August 7–11, 1990