ADM Worldvolume Geometry

TL;DR

This paper develops a geometric formalism based on the ADM approach to describe the dynamics of relativistic extended objects, like branes, in arbitrary backgrounds, providing a new Hamiltonian framework.

Contribution

It introduces an ADM-inspired geometric formalism for the Hamiltonian analysis of relativistic extended objects in arbitrary spacetimes, extending previous approaches.

Findings

Formulation of the dynamics using ADM geometry

Application to Dirac-Nambu-Goto objects in arbitrary backgrounds

Provides a new Hamiltonian framework for extended objects

Abstract

We describe the dynamics of a relativistic extended object in terms of the geometry of a configuration of constant time. This involves an adaptation of the ADM formulation of canonical general relativity. We apply the formalism to the hamiltonian formulation of a Dirac-Nambu-Goto relativistic extended object in an arbitrary background spacetime.