THE DYNAMICAL STRUCTURE OF HIGHER-DIMENSIONAL CHERN-SIMONS THEORY

Higher dimensional Chern-Simons theories, even though constructed alon g the same topological pattern as in 2 + 1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of fre edom. In this paper, we carry out the complete Dirac Hamiltonian analy sis (separation of first and second class constraints and calculation of the Dirac bracket) for a group G x U(1). We also study the algebra of surface charges that arise in the presence of boundaries and show t hat it is isomorphic to the WZW(4) discussed in the literature. Some a pplications are then considered. It is shown, in particular, that Chem -Simons gravity in dimensions greater than or equal to five has a prop agating torsion.