  We propose a prescription to quantize classical monomials in terms of
symmetric and ordered expansions of non-commuting operators of a bosonic
theory. As a direct application of such quantization rules, we quantize a
classically time evolved function
  $\mathcal{O}(q,p,t)$, and calculate its expectation value in coherent states.
The result can be expressed in terms of the application of a classical operator
which performs a {\em Gaussian smoothing} of the original function
$\mathcal{O}$ evaluated at the center of the coherent state. This scheme
produces a natural semi-classical expansion for the quantum expectation values
at a short time scale. Moreover, since the classical Liouville evolution of a
Gaussian probability density gives the {\bf same} form for the classical
statistical mean value, we can calculate the first order correction in $\hbar$
entirely from the associated classical time evolved function. This allows us to
write a general expression for the Ehrenfest time in terms of the departure of
the centroid of the quantum distribution from the classical trajectory provided
we start with an initially coherent state for each subsystem. In order to
illustrate this approach, we have calculated analytically the Ehrenfest time of
a model with $N$ coupled non-linear oscillators with non-linearity of even
order.
