Routh reduction for first-order field theories

TL;DR

This paper develops a reduction method for first-order Lagrangian field theories that incorporates momentum conservation, linking solutions of the original and reduced problems, with an illustrative example.

Contribution

It introduces a novel reduction framework for first-order field theories that explicitly accounts for conserved momenta, enhancing understanding of solution correspondence.

Findings

Established a relation between original and reduced solutions with fixed momentum.

Provided a detailed example illustrating the reduction process.

Demonstrated the applicability of the reduction theory to specific field theories.

Abstract

We present a reduction theory for first order Lagrangian field theories which takes into account the conservation of momenta. The relation between the solutions of the original problem with a prescribed value of the momentum and the solutions of the reduced problem is established. An illustrative example is discussed in detail.