Proof of the charge superselection rule in local relativistic quantum field theory

Abstract

The paper interprets and proves the charge superselection rule within the framework of local relativistic field theory as the statement that the charge operator commutes with all quasilocal observables. Once the basic formalism expressing the property of locality of the observables has been accepted, the proof is an elementary application of Gauss law relating the electric charge in a region to the flux of electric field through the boundary of the region. Most of the paper is devoted to the evidence that the indefinite metric formalism and its accompanying definitions of gauge, gauge transformation, and gauge invariance are internally coherent and consistent with the evidence from free field theory and the renormalized perturbation theory of coupled fields. The paper closes with speculations on analogous explanations of the baryon and lepton superselection rules within the framework of gauge models of strong and weak interactions.