  We show that quantum mechanics can be represented as an asymptotic projection
of statistical mechanics of classical fields. Thus our approach does not
contradict to a rather common opinion that quantum mechanics could not be
reduced to statistical mechanics of classical particles. Notions of a system
and causality can be reestablished on the prequantum level, but the price is
sufficiently high -- the infinite dimension of the phase space. In our approach
quantum observables, symmetric operators in the Hilbert space, are obtained as
derivatives of the second order of functionals of classical fields. Statistical
states are given by Gaussian ensembles of classical fields with zero mean value
(so these are vacuum fluctuations) and dispersion $\alpha$ which plays the role
of a small parameter of the model (so these are small vacuum fluctuations). Our
approach might be called {\it Prequantum Classical Statistical Field Theory} -
PCSFT. Our model is well established on the mathematical level. However, to
obtain concrete experimental predictions -- deviations of real experimental
averages from averages given by the von Neumann trace formula - we should find
the energy scale $\alpha$ of prequantum classical fields.
