  We consider the quantum partition function for a system of quantum spinors
and then derive an equivalent (or dual) classical partition function for some
scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a
model on 2-sphere configuration space), but the locality structure of the dual
system is preserved, in contrast to the imaginary time formalism. We also show
that the measure of integration in the classical partition function can be
formally expressed through relativistic Green's functions which suggests a
possible mechanism for the emergence of a classical space-time from
anti-commutativity of quantum operators.
