Classical and quantal nonrelativistic Chern-Simons theory

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Abstract
We construct a nonrelativistic field theory for the second-quantized N-body system of point particles with Chern-Simons interactions. Various properties of this model are discussed: its obvious and hidden symmetries, its relation to a relativistic field theory, and its supersymmetric formulation. We present classical, static solutions–solitons–that satisfy a self-dual equation, which is equivalent to the Liouville equation; hence, it is completely solvable. The dynamical role of the Chern-Simons interaction is demonstrated: the interaction does not merely change statistics but also provides the forces that bind the classical solitons.

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