## Realization of stochastic phase-space quantization on a collective field theory

We consider the collective-field-theoretical description of a many-body quantum system (one dimensional for simplicity). We show how the stochastic phase-space quantization prescriptions can be applied to such a system. We define integration measures for the inner product and prove, constructively, that it is not necessary to employ effective quantities (e.g., effective action, Hamiltonian, etc.) in this scheme, unlike the conventional formulation of collective field theory. We offer intuitive interpretations of these results in terms of particle spreading and minimum uncertainty. A specific, simple example is explicitly worked out.