Diffusion processes on path spaces with interactions

We construct dynamics on path spaces C(R;R) and C([-r,r];R) whose equilibri um states are Gibbs measures with free potential phi and interaction potent ial psi. We do this by using the Dirichlet form theory under very mild cond itions on the regularity of potentials. We take the carre du champ similar to the one of the Ornstein-Uhlenbeck process on C([0,infinity);R). Our dyna mics are non-Gaussian because we take Gibbs measures as reference measures. Typical examples of free potentials are double-well potentials and interac tion potentials are convex functions. In this case the associated infinite- volume Gibbs measures are singular to any Gaussian measures on C(R; R).