On dirichlet forms on topological vector spaces: Existence and maximality

Abstract

We recall basic problems of the theory of Dirichlet forms and symmetric Markov processes with finite or infinite dimensional state space. We discuss in particular the existence problem and give some new results concerning the structure of the space of Dirichlet forms extending a given minimal one. The results apply in particular to Dirichlet forms giving Hamiltonians of quantum mechanics and quantum field theory.