Canonical 3+1 Description of Relativistic Membranes

TL;DR

This paper presents a canonical 3+1 formulation of relativistic membranes, providing a non-local description that could extend string symmetries to higher dimensions and connect with gravity.

Contribution

It introduces a Hamiltonian reduction approach for relativistic membranes that generalizes string symmetries to higher-dimensional objects.

Findings

Non-local Hamiltonian description of membranes

Extension of string symmetries to higher dimensions

Potential link to gravitational theories

Abstract

$M$-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.