Lagrangian Reduction by Stages in Field Theory

TL;DR

This paper develops a geometric framework for Lagrangian reduction by stages in covariant field theory, extending concepts from mechanics and applying them to a molecular strand model.

Contribution

It introduces a new category of bundles for covariant field theory reduction, generalizing Lagrange-Poincaré bundles and analyzing reconstruction and Noether theorems.

Findings

Established a category of bundles for reduction in field theory.

Formulated the Noether theorem in this new context.

Applied the framework to a molecular strand with rotors.

Abstract

We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange-Poincar\'e bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame.