Canonical 3+1 Description of Relativistic Membranes

Abstract

$M$-dimensional extended objects $Σ$ can be described by projecting a Diff $Σ$ invariant Hamiltonian of time-independent Hamiltonian density {\cal H} onto the Diff $Σ$- singlet sector, which after Hamiltonian reduction, using {\cal H} itself for one of the gauge-fixing conditions, results in a non-local description that may enable one to extend the non-local symmetries for strings to higher dimensions and make contact with gravity at an early stage.