Scaling and Functional Integration. Brydges' Operator in Renormalization Theory

摘要

In previous papers, the authors introduced an axiomatic scheme for the functional211u001eintegrals used in quantum mechanics. Here, the authors extend this scheme to 211u001equantum field theory. Using a method recently introduced by Brydges, Hurd and 211u001eDimock, the authors consider a functional partial differential equation of 211u001eparabolic type which governs the renormalization group transformations. Unlike 211u001etheir predecessors, the authors deal directly with the theory in the Minkowski 211u001espace, without resorting to the Euclidean version and analytic continuation of 211u001eSchwinger functions. In physical terms, the scaling parameter is treated like an 211u001eadditional dimension for space-time.