Microscopic justification of the stochastic F-model of critical dynamics

We use a microscopic approach to derive the stochastic Langevin equations for a quantum Bose liquid near the phase transition to the superfluid state. These equations can be obtained in local form if either the finiteness of the system dimensions or the boundedness of the time interval under study is taken into account. We give the microscopic expressions for random forces in the stochastic equations and show that the white noise approximation holds only in the critical region. We prove that the model for properly describing the critical fluctuations is precisely the F-model.