  We study asymptotic expansions of Gaussian integrals of analytic functionals
on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an
asymptotic equality coupling the Gaussian integral and the trace of the
composition of scaling of the covariation operator of a Gaussian measure and
the second (Frechet) derivative of a functional. In this way we couple
classical average (given by an infinite-dimensional Gaussian integral) and
quantum average (given by the von Neumann trace formula). We can interpret this
mathematical construction as a procedure of ``dequantization'' of quantum
mechanics. We represent quantum mechanics as an asymptotic projection of
classical statistical mechanics with infinite-dimensional phase-space. This
space can be represented as the space of classical fields, so quantum mechanics
is represented as a projection of ``Prequantum Classical Statistical Field
Theory''.
