Towards a covariant canonical formulation for closed topological defects without boundaries

TL;DR

This paper develops a covariant canonical formalism for describing closed topological defects in curved spacetime, focusing on symplectic geometry and laying groundwork for future extensions.

Contribution

It introduces a covariant canonical framework specifically for closed topological defects without boundaries, advancing the geometric understanding of such defects.

Findings

Established symplectic structure for topological defects

Provided a covariant formalism compatible with curved backgrounds

Outlined potential directions for extending the framework

Abstract

On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We discuss the future extensions of the present results.