Towards an Analytic Theory of Stochastic and Quantum Fields

Abstract

We propose a method for the rigorous construction of physically relevant functional measures. In shaping it we get several conceptual insights, which can perhaps be summarized by the following statement: the renormalized interaction Lagrangian should be the generator of a flow on a space of asymptotically free cylinder functional measures with density given, in the case of Boson fields with polynomial self-interaction, by a generalized form of the Appell polynomials.