Time-dependent mean-field approximations for many-body observables

The excitation of a many-body system by a time-dependent perturbation is considered within the framework of functional integration. The stationary phase approximation to a functional-integral representation of the final expectation values of many-body observables in the interaction picture leads to a new time-dependent mean-field theory. The resulting equations of motion depend upon the observable itself and consequently are nonlocal in time. The method is illustrated by an analytically soluble application to the forced harmonic oscillator. NUCLEAR REACTIONS Functional integral representation of expectation values of many-body observables. Stationary phase approximation. Time-dependent mean fields.