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Abstract:
In these lectures I review classical aspects of the self-dual Chern-Simons systems which describe charged scalar fields in dimensions coupled to a gauge field whose dynamics is provided by a pure Chern-Simons Lagrangian. These self-dual models have one realization with nonrelativistic dynamics for the scalar fields, and another with relativistic dynamics for the scalars. In each model, the energy density may be minimized by a Bogomol'nyi bound which is saturated by solutions to a set of first-order self-duality equations. In the nonrelativistic case the self-dual potential is quartic, the system possesses a dynamical conformal symmetry, and the self-dual solutions are equivalent to the static zero energy solutions of the equations of motion. The nonrelativistic self-duality equations are integrable and all finite charge solutions may be found. In the relativistic case the self-dual potential is sixth order and the self-dual Lagrangian may be embedded in a model with an extended supersymmetry. The self-dual potential has a rich structure of degenerate classical minima, and the vacuum masses generated by the Chern-Simons Higgs mechanism reflect the self-dual nature of the potential.Note:
- 42 pages LaTeX
- lectures: Mt. Sorak 1994/06/27
- gauge field theory: Yang-Mills
- Chern-Simons term
- dimension: 3
- duality
- field equations: instanton
- operator: Lax
- vacuum state
- algebra: representation
- bibliography
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