Chern-Simons Field Theory and Completely Integrable Systems

Abstract

We show that the classical non-abelian pure Chern-Simons action is related in a natural way to completely integrable systems of the Davey-Stewartson hyerarchy, via reductions of the gauge connection in Hermitian spaces and by performing certain gauge choices. The Bäcklund Transformations are interpreted in terms of Chern-Simons equations of motion or, on the other hand, as a consistency condition on the gauge. A mapping with a nonlinear $\sigma$-model is discussed.

11 pages, Latex

References in corpus (1)

• Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets

Cited by in corpus (2)

• Integrable dissipative structures in the gauge theory of gravity
• Gauge Symmetry and Integrable Models