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

TL;DR

This paper develops a group-theoretic framework for relativistic charged particles and fluids, incorporating spin and magnetic effects, revealing new physical phenomena like spin precession due to pressure gradients.

Contribution

It introduces a unified symplectic and co-adjoint orbit approach to relativistic particle and fluid dynamics, including spin effects and novel spin precession phenomena.

Findings

Minimal coupling yields a gyromagnetic ratio of 2

Spin precession occurs due to pressure and energy density gradients

Euler equation is modified by spin density gradients

Abstract

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. The Euler equation (the dynamics of the velocity field) is also modified by gradients of the spin density.