Symplectic Structure in Brane Mechanics

TL;DR

This paper extends covariant canonical variational methods to brane dynamics, constructing a conserved symplectic current, and applies it to Dirac-Goto-Nambu branes without internal fields.

Contribution

It generalizes symplectic structure construction to brane mechanics, providing a covariant framework for analyzing brane dynamics.

Findings

Constructed a conserved bilinear symplectic current for branes.

Applied the formalism to Dirac-Goto-Nambu branes without internal fields.

Reviewed relationships between different variational approaches.

Abstract

This article treats the generalisation to brane dynamics of the covariant canonical variational procedure leading to the construction of a conserved bilinear symplectic current in the manner originally developped by Witten, Zuckerman and others in the context of field theory. After a general presentation, including a review of the relationships between the various (Lagrangian, Eulerian and other) relevant kinds of variation, the procedure is illustrated by application to the particularly simple case of branes of the Dirac-Goto-Nambu type, in which internal fields are absent.