Relativistic Guiding-Center Motion: Action Principle, Kinetic Theory, and Hydrodynamics

We treat the guiding-center dynamics in a non-uniform external Maxwell field using a manifestly Lorentz covariant action principle which easily reproduces the known Vandervoort equations of motion. We derive the corresponding kinetic theory and ideal hydrodynamic theory. In contrast to conventional five-equation hydrodynamics, the guiding-center hydrodynamics needs only three equations due to a constraint on the motion across magnetic field. We argue that this hydrodynamics applies more generally than the kinetic theory, e.g., for strongly-coupled quark-gluon plasma.