Covariant description of parametrized nonrelativistic Hamiltonian systems

TL;DR

This paper explores the covariant phase space formalism for parametrized nonrelativistic Hamiltonian systems, highlighting the freedom in choosing symplectic structures and constraints, and analyzing their impact on gauge transformations and observables.

Contribution

It introduces a covariant description of phase spaces in parametrized systems and examines the implications of symplectic and constraint choices within Dirac's formalism.

Findings

Covariant phase space formalism applied to parametrized systems

Freedom in symplectic structure and constraint choices analyzed

Impact on gauge transformations and observable algebra discussed

Abstract

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.