Time-dependent mean-field theory and quantized bound states

Abstract

A theory is presented in which approximations to quantum observables are obtained by applying the stationary-phase approximation to an exact functional integral representation of the many-body evolution operator. The requirement that the leading correction to the stationary-phase approximation vanish leads to a time-dependent Hartree-Fock mean field. Application of the theory to the Fourier transform of the trace of the evolution operator and the study of its poles yields quantized bound states with large amplitude. The theory is shown to reproduce the familiar static Hartree-Fock and random-phase approximations in the appropriate limits and yields an excellent approximation to the entire spectrum of the exactly solvable Lipkin model.