Unitarity, ghosts and nonminimal terms in Lorentz violating QED

TL;DR

This paper investigates the unitarity of a Lorentz-violating QED model with higher-order terms, identifying ghost states but demonstrating that perturbative unitarity can still be maintained in electron-positron scattering.

Contribution

It provides an explicit analysis of unitarity in a Lorentz-violating QED with nonminimal higher-order terms, showing conditions under which unitarity is preserved despite ghost states.

Findings

Ghost states are present due to higher-order terms.

Perturbative unitarity can be preserved in electron-positron scattering.

The model's unitarity depends on the treatment of ghost states.

Abstract

The unitarity of a Lorentz-invariance violating QED model with higher-order Myers and Pospelov photons coupled to standard fermions is studied. As expected, we find ghost states associated to the higher-order terms that may lead to the loss of unitarity. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to be preserved.