The Variational Problem and Background Field in the Renormalization Group Method for Nonlinear Sigma Models

Abstract

AbstractWe study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in $$d = 3, 4$$ d = 3 , 4 and adapt it to a class of nonlinear sigma models in $$d=2$$ d = 2 . The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis.