Use of Causality Conditions in Quantum Theory

It is shown that the derivation of the Kramers-Kronig dispersion relations given by Gell-Mann, Goldberger, and Thirring may be carried out without the use of perturbation theory. It is further shown that the results are essentially independent of the form of the coupling between the electromagnetic field and the matter fields. The demonstration is facilitated by the construction of simple rigorous expressions for the commutator of two vector potential operators and for the $S$-matrix describing photon scattering.