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This two-paper series addresses and fixes the long-standing gauge invarianceproblem of angular momentum in gauge theories. This QED part reveals: 1) Thespin and orbital angular momenta of electrons and photons can all beconsistently defined gauge invariantly. 2) These gauge-invariant quantities canbe conveniently computed via the canonical, gauge-dependent operators (e.g,$\psi ^\dagger \vec x \times\frac 1i \vec \nabla \psi$) in the Coulomb gauge,which is in fact what people (unconsciously) do in atomic physics. 3) Therenowned formula $\vec x\times(\vec E\times\vec B)$ is a wrong density for theelectromagnetic angular momentum. The angular distribution of angular-momentumflow 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 gaugetheories, and discuss the connection to nucleon spin structure.

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