Extended coupled-cluster method. I. Generalized coherent bosonization as a mapping of quantum theory into classical Hamiltonian mechanics

Abstract

The quantum-mechanical many-body problem is studied using the extended coupled-cluster method (ECCM) as a convenient parametrization of the Hilbert space. A systematic development of the formalism is given, and the quantum-mechanical problem is cast into the form of a classical Hamiltonian field theory in a complex symplectic phase space. The equations of motion of the basic ECCM amplitudes are derived both from a dynamical action principle using the ECCM average-value functional, and directly from the Schrödinger equation using the ECCM double similarity transformation. Rules are given for the construction of the Hamiltonian and other observables as well as their products. In particular, commutators are shown to be mapped into generalized classical Poisson brackets. The description is interpreted as an exact bosonization of the quantum theory in which the concept of bosonization is carried to the logical extreme, namely, the resulting generalized coherent bosons are identifiable with classical fields. The quantum-mechanical states of the system are points in the ECCM phase space, and their time evolution, or trajectories, are controlled by a classical Hamiltonian. The bosonization has a perturbation-theoretical basis in terms of maximally linked generalized tree diagrams. The increased degree of locality of the basic amplitudes allows applications to topological excitations and cases with spontaneous symmetry breaking.