Introduction

Abstract

The Non-Linear Sigma-Model (NLSM) is a field theory whose field takes its values in a Riemannian manifold M. The NLSM field values can therefore be considered as a set of coordinates in the internal manifold M whose metric is field-dependent. The NLSM format is thus the very general field-theoretical concept whose apparent geometrical meaning is the main reason for many successful applications of NLSM in field theory, string theory and statistical mechanics.