Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids

TL;DR

This paper derives Lagrangian and Hamiltonian formulations for ideal gauge-charged fluids using geometric reduction techniques, providing new insights into their mathematical structure and conservation laws.

Contribution

It introduces a novel geometric framework for gauge-charged fluids via Lagrangian and Hamiltonian reductions based on principal bundle automorphisms.

Findings

Derivation of equations of motion using Lagrangian and Poisson reductions

Establishment of a Kelvin-Noether theorem for these fluids

Formulation of a non-canonical Poisson bracket for the Hamiltonian structure

Abstract

The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of a principal bundle. As a consequence of the Lagrangian approach, a Kelvin-Noether theorem is obtained. The Hamiltonian formulation determines a non-canonical Poisson bracket associated to these equations.