Quantization of the Myers-Pospelov model: The photon sector interacting with standard fermions as a perturbation of QED

Abstract

We study the quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions. Our main objective, based upon experimental and observational evidence, is to construct an effective theory which is a genuine perturbation of QED, such that setting the Lorentz invariance violation parameters to zero will reproduce it. To this end we provide a physically motivated prescription, based on the effective character of the model, regarding the way in which the model should be constructed and how the QED limit should be approached. This amounts to the introduction of an additional coarse-graining physical energy scale $M$, under which we can trust the effective field theory formulation. The prescription is successfully tested in the calculation of the Lorentz invariance violating contributions arising from the electron self-energy. Such radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters and no fine-tuning problems are found. Microcausality violations are highly suppressed and occur only in a spacelike region extremely close to the light cone. The stability of the model is guaranteed by restricting to concordant frames satisfying $1\ensuremath{-}|{\mathbf{v}}_{\mathrm{max}}|>6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$.