Non-Abelian Fluid Dynamics in Lagrangian Formulation

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.Comment: 14 pp., REVTeX 4; a reference added; email correspondence to [email protected]

Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.Comment: Submitted to the Proceedings of the 3rd Symposium on Quantum Theory and Symmetries (QTS3) 10-14 September 2003. Preprint 9 pages including reference