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

Understand

We consider relativistic charged particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of co-adjoint orbits of the Poincar\'e group.

• The particle case is meant to clarify some points such as how minimal coupling (as defined in text) leads to a gyromagnetic ratio of $2$, 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.