Gauss’ Law and string-localized quantum field theory

Abstract

The quantum Gauss Law as an interacting field equation is a prominent feature of QED with eminent impact on its algebraic and superselection structure. It forces charged particles to be accompanied by “photon clouds” that cannot be realized in the Fock space, and prevents them from having a sharp mass [7, 19]. Because it entails the possibility of “measurement of charges at a distance”, it is well-known to be in conflict with locality of charged fields in a Hilbert space [3, 17]. We show how a new approach to QED advocated in [25, 26, 30, 31] that avoids indefinite metric and ghosts, can secure causality and achieve Gauss’ Law along with all its nontrivial consequences. We explain why this is not at variance with recent results in [8].