Chern-Simons Reduction and non-Abelian Fluid Mechanics

TL;DR

This paper introduces a non-Abelian extension of the Clebsch parameterization using Chern-Simons reduction, enabling a canonical symplectic formulation of non-Abelian fluid mechanics, advancing theoretical understanding of complex fluid systems.

Contribution

It presents a novel non-Abelian generalization of the Clebsch parameterization based on group-theoretical Chern-Simons reduction, providing a new framework for non-Abelian fluid mechanics.

Findings

Developed a non-Abelian Clebsch parameterization

Established a canonical symplectic structure for non-Abelian fluids

Connected Chern-Simons theory with fluid mechanics formalism

Abstract

We propose a non-Abelian generalization of the Clebsch parameterization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parameterization allows a canonical description of conventional fluid mechanics.