Angular Momentum in Electrodynamics
See also: Momentum (Particle in field)When describing the motion of a charged particle in an electromagnetic field, the canonical momentum P (derived from the Lagrangian for this system) is not gauge invariant. As a consequence, the canonical angular momentum L = r × p is not gauge invariant either. Instead, the momentum that is physical, the so-called kinetic momentum (used throughout this article), is (in SI units)
where e is the electric charge of the particle and A the magnetic vector potential of the electromagnetic field. The gauge-invariant angular momentum, that is kinetic angular momentum, is given by
The interplay with quantum mechanics is discussed further in the article on canonical commutation relations.
Read more about this topic: Angular Momentum