Unitarity in higher-order Lorentz-invariance violating QED

TL;DR

This paper investigates whether unitarity is preserved in a Lorentz-invariance violating QED model with higher-order photon terms, finding that unitarity can be maintained despite the presence of ghost states.

Contribution

It provides an explicit perturbative unitarity check in a higher-order Lorentz-violating QED, demonstrating conditions under which unitarity is preserved.

Findings

Ghost states are associated with higher-order terms but do not necessarily violate unitarity.

Explicit calculations show unitarity can be maintained in electron-positron scattering.

The study clarifies the impact of higher-order Lorentz-violating terms on quantum consistency.

Abstract

The unitarity in Lorentz invariance violating QED consisting of standard fermions and higher-order photons of the Myers-Pospelov theory is studied. We find ghost states associated to the higher-order character of the theory which could render the $S$ matrix nonunitary. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to preserve unitarity.