Renormalization of the vector current in QED
Abstract
It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the fourdivergence of the electromagnetic fieldstrength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the MS̄renormalized current by a definite finite renormalization. This happens in such a way that Gauss’s law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory.
 Publication:

Physical Review D
 Pub Date:
 May 2006
 DOI:
 10.1103/PhysRevD.73.105019
 arXiv:
 arXiv:hepth/0512187
 Bibcode:
 2006PhRvD..73j5019C
 Keywords:

 11.40.q;
 11.10.Gh;
 11.30.j;
 12.20.m;
 Currents and their properties;
 Renormalization;
 Symmetry and conservation laws;
 Quantum electrodynamics;
 High Energy Physics  Theory;
 High Energy Physics  Phenomenology
 EPrint:
 9 pages. Corresponds to published version (Phys. Rev. D), including appendix about Weeks's paradox