Charged particles in external fields

The second-quantized Dirac and Klein-Gordon equations with external fields are solved. It is shown that the interpolating field is local and satisfies the Yang-Feldman equations. The Capri-Wightman approach and the Friedrichs-Segal approach are shown to lead to the same unitaryS-operator. The evolution operator andS-operator are studied. A divergence-free perturbation expansion of theS-operator is derived and the connection with the Feynman-Dyson series is established.