The Variational Problem and Background Field in the Renormalization Group Method for Non-Linear Sigma Models

Abstract

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

Comments: Proof of Theorem 1 reorganized, some changes in symmetry subgroup section, other minor changes. 20 pages