Routh reduction and Cartan mechanics

TL;DR

This paper develops a Cartan mechanics approach to Routh reduction, aiming to extend it to field theories, motivated by integrable systems and Hamiltonian reduction of WZNW models.

Contribution

It introduces a Cartan mechanics formulation for Routh reduction and applies it to Lagrangian Adler-Kostant-Symes systems, advancing the theoretical framework.

Findings

Formulation of Routh reduction within Cartan mechanics.

Application to integrable systems and WZNW field theories.

Extension of Routh reduction techniques to field theory contexts.

Abstract

In the present work a Cartan mechanics version for Routh reduction is considered, as an intermediate step toward Routh reduction in field theory. Motivation for this generalization comes from an scheme for integrable systems [12], used for understanding the occurrence of Toda field theories in so called Hamiltonian reduction of WZNW field theories [11]. As a way to accomplish with this intermediate aim, this article also contains a formulation of the Lagrangian Adler-Kostant-Symes systems discussed in [12] in terms of Routh reduction.