On the stochastic quantisation of Yang-Mills field theory

Abstract

A new functional approach to the stochastic quantisation of continuum Euclidean Yang-Mills field theory is presented. Non-negative integral representations for the nonequilibrium and equilibrium probability distributions are given. A new dynamical generating function is proposed and its equilibrium limit is obtained. The new dynamical Feynman rules for the generating function are derived and the superficial renormalisability of the theory is studied. Euclidean volume divergences appear. The cancellations of the latter for an Euclidean dimensions d, and, for d=4, that of all quartic ultraviolet divergences, are carried out.