1+1-dimensional Yang-Mills equations and mass via quasiclassical correction to action

Abstract

Two-dimensional Yang-Mills models in a pseudo-euclidean space are considered from a point of view of a class of nonlinear Klein-Gordon-Fock equations. It is shown that the Nahm reduction does not work, another choice is proposed and investigated. A quasiclassical quantization of the models is based on Feynmann-Maslov path integral construction and its zeta function representation in terms of a Green function diagonal for an auxiliary heat equation with an elliptic potential. The natural renormalization use a freedom in vacuum state choice as well as the choice of the norm of an evolution operator eigenvectors. A nonzero mass appears via the quasiclassical correction.