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

TL;DR

This paper investigates the Lorentz invariance of the Dyson series in theories with derivative couplings, specifically in scalar electrodynamics and renormalized ^4 theory, providing evidence that standard Feynman rules remain applicable.

Contribution

It demonstrates that Lorentz invariance holds for the Dyson series with derivative couplings and confirms the validity of usual Feynman rules in these cases.

Findings

Lorentz invariance is preserved in the Dyson series with derivative couplings.

Standard Feynman rules can be applied to such theories.

Evidence supports the consistency of these approaches in scalar electrodynamics and ^4 theory.

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.