Simplectic geometry and the canonical variables for Dirac-Nambu-Goto and Gauss-Bonnet system in string theory

TL;DR

This paper identifies canonical variables for Dirac-Nambu-Goto and Gauss-Bonnet systems in string theory using a covariant formalism and geometric structures on phase space.

Contribution

It introduces a covariant, gauge-invariant geometric framework to determine canonical variables for DNG and GB systems in string theory.

Findings

Canonical variables for DNG and GB systems are explicitly identified.

The formalism is covariant and gauge-invariant, ensuring consistency in curved backgrounds.

Outlines potential extensions of the geometric approach.

Abstract

Using a strongly covariant formalism given by Carter for the deformations dynamics of p-branes in a curved background and a covariant and gauge invariant geometric structure constructed on the corresponding Witten's phase space, we identify the canonical variables for Dirac-Nambu-Goto [DNG] and Gauss-Bonnet [GB] system in string theory. Future extensions of the present results are outlined.