Topological field theories and integrable models

We show that the classical non-Abelian pure Chern–Simons action is related to nonrelativistic models in (2+1) dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern–Simons fields, associated with the isotropy subgroup of the considered symmetric space. Thus a relation between the Chern–Simons theory and the Davey–Stewartson hierarchy is established in a natural way. The Bäcklund transformations are interpreted in terms of Chern–Simons constraints. Moreover, certain nonintegrable Heisenberg models can be embedded into the pure Chern–Simons theory. The main classical and quantum properties of these systems are discussed.