Some Perspectives on the Nonlinear Sigma Model

Abstract

When the nonlinear sigma model was first written down in 1959 by Feza Gursey [1], it was modestly offered as “an illustration of the possibility that the symmetries of the weak interactions may be essentially contained in those of the strong interactions, and certainly not as a definite proposal for a theory of elementary particles.” In the more than twenty years since that paper appeared, the nonlinear sigma model has been extended in several ways, applied to a variety of low energy phenomena, and analyzed as both a classical and quantum field theory. While it has never gained the status of a fundamental theory of elementary particles, it has certainly played a key role in the development of particle physics. Its beautiful and realistic symmetry properties and its deep dynamical structure have made it much more than an illustration of possibilities.