Symplectic structure for elastic and chiral conducting cosmic string models

TL;DR

This paper develops a covariant formalism to construct the symplectic structure for elastic and chiral cosmic string models, clarifying their mathematical properties and integrability in curved spacetime.

Contribution

It introduces a conserved symplectic current for elastic string models and analyzes various formulations of chiral strings, enhancing understanding of their integrability and dynamics.

Findings

Constructed a conserved symplectic current for elastic string models

Analyzed different formulations of chiral string actions

Clarified the integrability of chiral strings in curved spacetime

Abstract

This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman and others in the context of field theory. After recalling the basic principles of this procedure, we construct the conserved bilinear symplectic current for generic elastic string models. These models describe current carrying cosmic strings evolving in an arbitrary curved background spacetime. Particular attention is paid to the special case of the chiral string for which the worldsheet current is null. Different formulations of the chiral string action are discussed in detail, and as a result the integrability property of the chiral string is clarified.