Spin and orbital angular momentum in gauge theories (I): QED and determination of the angular momentum density

Abstract

This two-paper series addresses and fixes the long-standing gauge invariance problem of angular momentum in gauge theories. This QED part reveals: 1) The spin and orbital angular momenta of electrons and photons can all be consistently defined gauge invariantly. 2) These gauge-invariant quantities can be conveniently computed via the canonical, gauge-dependent operators (e.g, ${\psi }^{†}\vec{x}\times \frac{1}{i}\vec{\nabla }\psi$) in the Coulomb gauge, which is in fact what people (unconsciously) do in atomic physics. 3) The renowned formula $\vec{x}\times (\vec{E}\times \vec{B})$ is a wrong density for the electromagnetic angular momentum. The angular distribution of angular-momentum flow in polarized atomic radiation is properly described not by this formula, but by the gauge invariant quantities defined here. The QCD paper [arXiv:0907.1284] will give a non-trivial generalization to non-Abelian gauge theories, and discuss the connection to nucleon spin structure.

Comments: 3 pages, no figure; in series with ``Spin and orbital angular momentum in gauge theories (II): QCD and nucleon spin structure'', arXiv:0709.1284[hep-ph]