Hamiltonian Reduction of Diffeomorphism Invariant Field Theories

For a variety of diffeomorphism–invariant field theories describing hypersurface motions (such as relativistic M -branes in space-time dimension M + 2) we perform a Hamiltonian reduction “at level 0”, showing that a simple algebraic function of the normal velocity is canonically conjugate to the shape Σ of the hypersurface. The Hamiltonian dependence on Σ is solely via the domain of integration, raising hope for a consistent, reparametrisation–invariant quantization. Heisenberg Fellow. On leave of absence from Karlsruhe University. Permanent address: Department of Mathematics, University of California, Santa Cruz, CA 95064, USA, Research partially supported by NSF Grant DMS-9503273 and DOE contract DE-FG03-95ER25245-A000.