CHERN-SIMONS QUANTUM-MECHANICS

The Chern-Simons action for three-dimensional gauge theories is a special case of a particle mechanics 'sigma model Chern-Simons' action with a sympletic target space. The authors discuss the classical and quantum mechanics of this action and its (N-extended) supersymmetric generalisations. They show further that the N=1 supersymmetric Chern-Simons term can be used to cancel the global anomaly that arises in the standard supersymmetric sigma model when the target space is not a spin manifold. A new global anomaly arises, however, if the target space does not admit a spinc structure.