Identically closed two-form for covariant phase space quantization of Dirac-Nambu-Goto p-branes in a curved spacetime

TL;DR

This paper establishes a covariant symplectic structure on the phase space of Dirac-Nambu-Goto p-branes in curved spacetime, providing a foundation for their covariant quantization.

Contribution

It proves the existence of a covariant symplectic form on the phase space of p-branes using Carter's formalism, enabling covariant quantization approaches.

Findings

Phase space has a covariant symplectic structure.

Formalism applies to p-branes in curved backgrounds.

Provides basis for covariant phase space quantization.

Abstract

Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant symplectic structure, which can serve as a starting point for a phase space quantization of such objects. Some open questions for further research are outlined.