Polarization operator in quantum electrodynamics with a pair-creating external field

We consider various radiative processes with a single-photon initial state in the framework of quantum electrodynamics with a pair-creating external field. We show that the probabilities of such processes can be expressed in terms of the various polarization operators. In the case of a constant field we calculate the polarization operator pi-tilde/sub ..mu..//sub ..nu../(k-italic), which has not been considered before and which is expressed in terms of the so-called causal Green function S-italic-tilde/sup c-italic/(x-italic,x-italic') of the electron. This polarization operator appears in the expression for the probability of producing N-italic random pairs by a photon.