Hamiltonian Reduction of Diffeomorphism Invariant Field

TL;DR

This paper performs a Hamiltonian reduction of diffeomorphism-invariant hypersurface theories, revealing a simple conjugate variable to shape and suggesting a path toward reparametrization-invariant quantization.

Contribution

It introduces a Hamiltonian reduction method for diffeomorphism-invariant field theories, identifying a canonical conjugate to hypersurface shape.

Findings

Normal velocity's algebraic function is conjugate to shape .

Hamiltonian depends only on the domain of integration.

Results support potential for reparametrization-invariant quantization.

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