Action Principle for Relativistic Magnetohydrodynamics

A covariant action principle for ideal relativistic magnetohydrodynamics in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al. [Ann. Phys. 169, 29 (1986)], which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant byproducts of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory.