Classical quantization condition in the generalized coherent-state representation with application to many-body systems

On the basis of the ansatz of the single-valuedness for the classically approximated wave function, a classical quantization rule is derived for a dynamical system described by a general class of coherent states. The classical wave function, which is defined on the manifold parametrizing the coherent states, is constructed by an application of the stationary phase approximation to the coherent-state path integral. The general form of the quantization rule for the time-dependent Hartree-Fock solutions is obtained as a particular case.