  Motivated by applications to quantum field theory we consider Gibbs measures
for which the reference measure is Wiener measure and the interaction is given
by a double stochastic integral and a pinning external potential. In order
properly to characterize these measures through DLR equations, we are led to
lift Wiener measure and other objects to a space of configurations where the
basic observables are not only the position of the particle at all times but
also the work done by test vector fields. We prove existence and basic
properties of such Gibbs measures in the small coupling regime by means of
cluster expansion.
