Gauge Symmetries, Contact Reduction, and Singular Field Theories

TL;DR

This paper extends symmetry reduction methods to singular Lagrangian field theories using multisymplectic formalism, with applications to classical models and insights into General Relativity.

Contribution

It develops a formalism for symmetry reduction of singular Lagrangian field theories within the De-Donder Weyl multisymplectic framework, broadening classical reduction techniques.

Findings

Extended reduction formalism to singular Lagrangian models.

Applied the framework to physically-motivated examples.

Discussed implications for classical General Relativity.

Abstract

The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings leads to a dynamically-equivalent theory, which is frictional in nature. In this article, we extend the formalism to physical models, of both particles and fields, described by singular Lagrangians. In order to work with a finite-dimensional (velocity) phase space, our construction requires that we treat classical field theories within the De-Donder Weyl formalism, in which a multisymplectic structure is introduced on the first jets of the bundle of fields. The results obtained are subsequently applied to a number of physically-motivated examples, as well as a discussion presented on the implications of our work for classical General Relativity.