A Path Integral Formalism of Collective Motion

Abstract

A quantum mechanical formalism of collective motion is proposed by using the idea of path integral method. Time evolution of many-body system is described by the propagator which joins the many-body state vectors parametrized by complex collective parameters. A general form of path integral representation for the propagator is derived in the complex parameter space. In particular the case of the coherent state representation is discussed in detail. It is pointed out that the time-dependent variation principle and especially the time dependent Hartree-Fock are naturally obtained as a classical limit.