Causal Stepanov–Bogoliubov’s interacting fields for Yukawa’s model

We explore the properties of Stepanov–Bogoliubov’s interacting fields in the perturbative regime in the axiomatic framework of causal perturbation theory. Considering the particular and important case of Yukawa’s model that we have previously studied in the causal approach, we show the axiomatic construction of the local dynamical variables, among which the interacting fields are of most interest, and their perturbative realization in the causal approach. We prove that they satisfy interacting equations of motion at all orders in perturbation theory only if the local currents are correctly constructed. Additionally, we show that they satisfy modified Källén–Yang–Feldman’s equations, as a consequence of which the scattering operator in causal perturbation theory satisfies the definition given by Källén.