In these lectures I review classical aspects of the self-dual Chern-Simons
systems which describe charged scalar fields in 2+1 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.Comment: 42 pages LaTe
