Radiative processes in an external pair-producing electromagnetic field

A study is made of some aspects of the calculation of the total probabilities of transitions from the vacuum and single-electron states in quantum electrodynamics in an external pair-producing field. These aspects are associated with the occurrence of new transition channels due to particle production from the vacuum. General expressions are derived for the probabilities of transitions from the vacuum state and the single-electron state. It is shown that these probabilities are determined by the imaginary parts of the corresponding Feynman diagrams with certain propagators of the electron in the external field. Calculations are made for the case of a constant electric field