Diffeomorphism groups and current algebras: Configuration space analysis in quantum theory

The constuction of models of non-relativistic quantum fields via current al gebra representations is presented using a natural differential geometry of the configuration space Gamma of particles, the corresponding classical Di richlet operator associated with a Poisson measure on Gamma, being the free Hamiltonian. The case with interactions is also discussed together with it s relation to the problem of unitary representations of the diffeomorphism group on R-d.