Hamiltonian Reduction of Diffeomorphism Invariant Field

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 \Sigma of the hypersurface. The Hamiltonian dependence on \Sigma is solely via the domain of integration, raising hope for a consistent, reparametrisation-invariant quantization.