  We show that QM can be represented as a natural projection of a classical
statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real
Hilbert space. Statistical states are given by Gaussian measures on $\Omega$
having zero mean value and dispersion of the Planck magnitude -- fluctuations
of the ``vacuum field.'' Physical variables (e.g., energy) are given by maps
$f: \Omega \to {\bf R}$ (functions of classical fields). The crucial point is
that statistical states and variables are symplectically invariant. The
conventional quantum representation of our prequantum classical statistical
model is constructed on the basis of the Teylor expansion (up to the terms of
the second order at the vacuum field point $\omega=0)$ of variables $f: \Omega
\to {\bf R}$ with respect to the small parameter $\kappa= \sqrt{h}.$ A Gaussian
symplectically invariant measure (statistical state) is represented by its
covariation operator (von Neumann statistical operator). A symplectically
invariant smooth function (variable) is represented by its second derivative at
the vacuum field point $\omega=0.$ From the statistical viewpoint QM is a
statistical approximation of the prequantum classical statistical field theory
(PCSFT). Such an approximation is obtained through neglecting by statistical
fluctuations of the magnitude $o(h), h\to 0,$ in averages of physical
variables. Equations of Schr\"odinger, Heisenberg and von Neumann are images of
dynamics on $\Omega$ with a symplectically invariant Hamilton function.
