Non-Abelian Fluid Dynamics in Lagrangian Formulation

TL;DR

This paper develops a Lagrangian formulation for non-Abelian fluid dynamics, extending classical fluid models to include non-Abelian gauge fields, with potential applications to quark-gluon plasma physics.

Contribution

It introduces a symplectic/Lagrangian framework for non-Abelian fluids, incorporating gauge covariant charges and Wong equations, advancing theoretical understanding of such complex systems.

Findings

Formulation of non-Abelian fluid equations in Lagrangian form

Derivation of a Lorentz force law for non-Abelian charges in fluid flow

Establishment of a gauge covariant charge evolution equation (Wong equation)

Abstract

Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic/Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form well known in Lie group theory. In our simplest model the fluid flows with velocity v and in presence of non-Abelian chromoelectric/magnetic E^a / B^a fields, the fluid feels a Lorentz force of the form Q_a E^a + (v / c) \times Q_a B^a, where Q_a is a space-time local non-Abelian charge satisfying a fluid Wong equation [ (D_t + v \cdot D) Q ]_a = 0 with gauge covariant derivatives.