Effective Euler–Heisenberg Lagrangians in models of QED

Abstract

The main goal of this paper is a direct diagrammatic evaluation of the effective four-photon Lagrangian of the Euler–Heisenberg type for the quantum electrodynamics of massive charged vector bosons. This QED model is naturally embedded in the standard electroweak theory, and we have carried out the corresponding one-loop calculation in the unitary gauge. As far as we know, such a work has not been published before since usually the R-gauge techniques are preferred for the computation of loop Feynman diagrams. We have recovered the result obtained many years ago by Vanyashin and Terent’ev, who used a specific functional method. For completeness and for validation of our techniques, we have also redone the analogous calculations for scalar and spinor QED.