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We consider relativistic charged particle dynamics and relativisticmagnetohydrodynamics using symplectic structures and actions given in terms ofco-adjoint orbits of the Poincar\'e group. The particle case is meant toclarify some points such as how minimal coupling (as defined in text) leads toa gyromagnetic ratio of $2$, and to set the stage for fluid dynamics. Thegeneral group-theoretic framework is further explained and is then used to setup Abelian magnetohydrodynamics including spin effects. An interesting newphysical effect is precession of spin density induced by gradients in pressureand energy density. The Euler equation (the dynamics of the velocity field) isalso modified by gradients of the spin density.

Relativistic Particle and Relativistic Fluids: Magnetic Moment and Spin-Orbit Interactions