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 ${\varphi }^4$ theory. We eventually give evidence that Lorentz invariance is satisfied and that usual Feynman rules can be applied to the interaction Lagrangian.

arXiv comment15 pages; improved Introduction and added two references; improved proofs in Section 3 and 4