PUB - Publikationen an der Universität Bielefeld

We derive the precise relation of the internal differential geometry of Poisson spaces developed in [1] to the corresponding external geometry given by the associated Fock structure. In particular, we identify the (internal) Laplace-Beltrami operator H-pi sigma(Gamma) on Poisson space as the second quantization of the Laplacian on R(d). Furthermore, the diffusion process generated by H-pi sigma(Gamma), which is a kind of distorted Brownian motion on the configuration space, is described explicitly. All this generalizes to the case where the underlying Euclidean space R(d) is replaced by an (infinite-dimensional) manifold.