Hamiltonian Reduction of Diffeomorphism Invariant Field

Abstract

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