Causal Stepanov–Bogoliubov’s interacting fields of light-front quantum electrodynamics

We explore the properties of Stepanov–Bogoliubov’s interacting fields in the framework of null-plane causal perturbation theory. Considering light-front quantum electrodynamics, that have been previously studied in this framework, and extending the results from there, we show that, contrary to what occurs in instant dynamics, in light-front dynamics the interacting equations of motion are satisfied only in the adiabatic limit for the fields whose Feynman’s propagators acquire an instantaneous term in the splitting of their (anti-)commutation distribution. The null-plane gauge condition, on the other hand, can be imposed on the interacting electromagnetic field for every switching function, at all orders of perturbation theory. We also show that the interacting fields satisfy finite Källén–Yang–Feldman’s equations that are formally independent of the normalization of the retarded distributions.