Editing Angular momentum (section)

== Angular momentum in electrodynamics ==
{{See also|Momentum#Particle_in_a_field|l1=Momentum (Particle in field)}}

When describing the motion of a [[charged particle]] in an [[electromagnetic field]], the [[canonical momentum]] '''P''' (derived from the [[Lagrangian mechanics|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]])
<math display="block"> \mathbf{p} = m\mathbf{v} = \mathbf{P} - e \mathbf{A} </math>
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
<math display="block">\mathbf{K}= \mathbf{r} \times ( \mathbf{P} - e\mathbf{A} )</math>

The interplay with quantum mechanics is discussed further in the article on [[canonical commutation relation]]s.