  $M$-dimensional extended objects $\Sigma$ can be described by projecting a
Diff $\Sigma$ invariant Hamiltonian of time-independent Hamiltonian density
{\cal H} onto the Diff $\Sigma$- 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.
