A non-perturbative approach to the infrared problem in QED: Construction of charged states

A non-perturbative treatment of the infrared problem in quantum electrodynamics is presented. Starting from the local and covariant correlation functions of the Gupta-Bleuler formulation an explicit construction of the physical charged states is given. They are shown to satisfy a non-(Lorentz) covariant infrared condition, of Bloch-Nordsieck type, compatible with the Gupta-Bleuler condition (resolution of Zwanziger's paradox). The breaking of the Lorentz group in the charged sectors and its physical meaning is explained. The infrared structure of the S-matrix elements between physical charged states is shown to be that of the classical Bloch-Nordsieck factors, (proof of the Bloch-Nordsieck ansatz), and to be simply related to that calculated by using local covariant states.