Chern-Simons Reduction and non-Abelian Fluid Mechanics

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.

Comments: 12 pages, REVTeX; revised for publication in Phys Rev D; email to jackiw@mitlns.mit.edu