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Abstract In the paper the perturbation theory is constructed for QED, for which the interaction with the external pair‐creating field is kept exactly. An explicit expression for the perturbation theory causal electron propagator is found. Special features of usage of the unitarity conditions for calculating the total probabilities of radiative processes in the case are discussed. Exact Green functions are introduced and the functional formulation is discussed. Perturbation theory for calculating the mean values of the Heisenberg operators, in particular, of the mean electromagnetic field is built in the case under consideration. Effective Lagrangian which generates the exact equation for the mean electromagnetic field is introduced. Functional representations for the generating functionals introduced in the paper are discussed.
Fradkin et al. (Thu,) studied this question.