On the Lorentz-invariance of the Dyson series in theories with derivative couplings

Abstract: We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $\phi ^4$ theory. We eventually give evidence that Lorentz invariance is satisfied and that usual Feynman rules can be applied to the interaction Lagrangian.