Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic or 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 $\mathbf{v}$ and, in the presence of non-Abelian chromoelectric or magnetic ${\mathbf{E}}^a/{\mathbf{B}}^a$ fields, the fluid feels a Lorentz force of the form $Q_a{\mathbf{E}}^a+(\mathbf{v}/c)\times Q_a{\mathbf{B}}^a,$ where $Q_a$ is a space-time local non-Abelian charge satisfying a fluid Wong equation $[{(D}_t+\mathbf{v}\cdot \mathbf{D})Q{]}_a=0\mathrm{}$ with gauge covariant derivatives.

• Received 16 October 2002

DOI:https://doi.org/10.1103/PhysRevD.67.025013