Gibbs measures on Brownian currents

Details Gibbs measures on Brownian currents Gibbs measures on Brownian currents

2007-04-24

arxiv.org/abs/0704.3237v1

Physics

Mathematical Physics

51 pages

Scientific paper

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.

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