We consider relativistic charged-particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of coadjoint orbits of the Poincaré group. The particle case is meant to clarify some points such as how minimal coupling (as defined in the text) leads to a gyromagnetic ratio $g=2$ and to set the stage for fluid dynamics. The general group-theoretic framework is further explained and is then used to set up Abelian magnetohydrodynamics including spin effects. An interesting new physical effect is precession of spin density induced by gradients in pressure and energy density. The Euler equation (the dynamics of the velocity field) is also modified by gradients of the spin density.

• Received 22 June 2014

DOI:https://doi.org/10.1103/PhysRevD.90.105018