  We construct a field theory to describe energy averaged quantum statistical
properties of systems which are chaotic in their classical limit. An expression
for the generating function of general statistical correlators is presented in
the form of a functional supermatrix nonlinear $\sigma$-model where the
effective action involves the evolution operator of the classical dynamics.
Low-lying degrees of freedom of the field theory are shown to reflect the
irreversible classical dynamics describing relaxation of phase space
distributions. The validity of this approach is investigated over a wide range
of energy scales. As well as recovering the universal long-time behavior
characteristic of random matrix ensembles, this approach accounts correctly for
the short-time limit yielding results which agree with the diagonal
approximation of periodic orbit theory.
