The Photon Sector in the Quantum Myers-Pospelov Model: An improved description

TL;DR

This paper develops an effective quantum theory for the photon sector in the Myers-Pospelov model, incorporating a low energy scale to perturbatively extend QED while respecting experimental bounds on Lorentz invariance violation.

Contribution

It introduces a novel prescription for quantizing the photon sector with LIV parameters, ensuring a proper QED limit and consistent radiative corrections without fine-tuning.

Findings

LIV corrections are suppressed by small factors for reasonable parameters.

The approach reproduces standard QED when LIV parameters are zero.

The chosen scale M aligns with electroweak symmetry breaking, satisfying experimental constraints.

Abstract

The quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions is studied. Our main objective is to construct an effective quantum theory that results in a genuine perturbation of QED, such that setting zero the Lorentz invariance violation (LIV) parameters will reproduce it. This is achieved by introducing an additional low energy scale $M$, together with a physically motivated prescription to take the QED limit. The prescription is successfully tested in the calculation of the electron self-energy in the one loop approximation. The LIV radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters, no fine-tuning problems are found at this stage and the choice for $M$ to be of the order of the electroweak symmetry breaking scale is consistent with the stringent bounds for the LIV parameters, in particular with those arising from induced dimension three operators.