Spin and orbital angular momentum in gauge theories (I): QED and determination of the angular momentum density
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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, $ψ^\dagger \vec x \times\frac 1i \vec \nabla ψ$) 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.
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]
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]