Non-symmetric perturbations of symmetric Dirichlet forms

We provide a path-space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local Dirichlet form. The representation is a combination of Feynman–Kac and Girsanov formulas, and extends previously known results in the framework of symmetric diffusion processes through the use of the Hardy class of smooth measures, which contains the Kato class of smooth measures.