Basic symplectic geometry for p-branes with thickness in a curved background

TL;DR

This paper develops a covariant canonical formalism for p-branes with thickness in curved backgrounds by constructing a symplectic structure on the phase space, facilitating potential quantization approaches.

Contribution

It introduces a symplectic potential for thick p-branes in curved backgrounds, enabling a covariant phase space formulation crucial for quantization.

Findings

Established a symplectic structure on the phase space of p-branes with thickness.

Provided a covariant description of the canonical formalism.

Highlighted the role of the symplectic potential in phase space analysis.

Abstract

We show that the Witten covariant phase space for p-branes with thickness in an arbitrary background is endowed of a symplectic potential, which although is not important to the dynamics of the system, plays a relevant role on the phase space, allowing us to generate a symplectic structure for the theory and therefore give a covariant description of canonical formalism for quantization.