DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS I: CONSTRUCTION AND QFT EXAMPLES

Abstract

Random fields are given in terms of measures which (in general) are singular with respect to that of white noise. However, many such measures can be expressed in terms of white noise through a positive generalized functional acting as a generalized Radon-Nikodym derivative. We give criteria for this to be the case and show that these criteria are fulfilled by Schwinger and Wightman functionals of various nontrivial quantum field theory models. Furthermore a number of closability criteria are given and discussed for the Dirichlet forms associated with positive generalized functionals of white noise. In a second paper we apply these results to the construction of Markov and of quantum fields.