Nonabelian fluids and helicities

TL;DR

This paper introduces non-Abelian fluid helicities, extending gauge helicity concepts to fluid systems with non-Abelian gauge fields, and derives their conservation laws and equations of motion.

Contribution

It defines non-Abelian fluid helicities and total helicities, formulates Lagrangian and Hamiltonian descriptions, and derives conserved Euler-Yang-Mills equations for gluonic fluids.

Findings

Defined non-Abelian fluid helicities for gluonic and quark fluids

Derived Lagrangian and Hamiltonian formulations for coupled systems

Established conservation of helicities in non-Abelian fluid dynamics

Abstract

In analogy with the non-Abelian gauge helicities conserved in time for ``null fields", that we have defined previously, in this paper we first define non-Abelian fluid helicities and then total non-Abelian helicities for combined non-Abelian fluid and gauge fields. For a U(N) group the helicities considered are for both gluonic-type fluids, composed of particles in the adjoint representation, and quark-type fluids, in the $N$-dimensional Cartan subalgebra. We write down various Lagrangian formulations for the uncoupled and coupled systems. In each case we determine the equations of motion, symmetries, and a Hamiltonian formulation. Taking the velocity of the fluid in the adjoint representation, we find that in the case of the gluonic fluid, we can write a non-Abelian gluonic fluid Euler-Yang-Mills equation that conserves the defined helicities, and comes from a Lagrangian.