Renormalization Of High-Energy Lorentz Violating QED

TL;DR

This paper investigates a Lorentz-violating extension of QED that remains unitary and super-renormalizable, analyzing its renormalization properties and implications for the hierarchy problem.

Contribution

It introduces a high-energy Lorentz-violating QED model with higher-dimension operators and analyzes its one-loop renormalization, showing how divergences can be controlled.

Findings

Power-like divergences are multiplied by arbitrary constants.

High-energy divergences can be set to zero, bypassing the hierarchy problem.

The model is unitary, CPT invariant, and super-renormalizable.

Abstract

We study a QED extension that is unitary, CPT invariant and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations at high and low energies and analyse the relation between them. It emerges that the power-like divergences of the low-energy theory are multiplied by arbitrary constants, inherited by the high-energy theory, and therefore can be set to zero at no cost, bypassing the hierarchy problem.