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

X.S. Chen, X.F. Lü, W.M. Sun, F. Wang, T. Goldman
2007 arXiv   pre-print
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, $\psi ^\dagger \vec x \times\frac 1i \vec \nabla \psi$) in the Coulomb gauge, which is in fact what people
more » ... ) 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.
arXiv:0709.3649v1 fatcat:krhq2ag5yjg4lktsh4qomzphfm