Nonlocal hydrodynamics in the quantum field model $\varphi^4$

A procedure of passing from the quantum statistic mechanics to hydrodynamics previously found by the author is applied to the quantum field model $\varphi^4$. In a certain class of external forces the equations of the quantum many-body system are shown to be equivalent to the equations of the nonlocal hydrodynamics. Hydrodynamic nonlocalities arising in the constituent relations are expressed via Green's functions for currents. By using the general symmetry properties a number of properties for the nonlocality kernels is deduced. In particular, conditions related to dissipativity and to $T$-invariance of the $\varphi 4$ model (an analogue of Onsager's relations) are established. The connection of the classical transport coefficients with the nonlocality kernels is found. An algorithm for calculating the constituent relations by the perturbation theory on a base of the technique of temperature Green's functions is described.