# Gauge field theories with Lorentz-violating operators of arbitrary dimension

## TL;DR

This paper classifies Lorentz- and CPT-violating operators in nonabelian gauge theories, constructing gauge-invariant terms and applying the results to derive experimental constraints in QED and QCD.

## Contribution

It provides a comprehensive classification of Lorentz- and CPT-violating operators of arbitrary dimension in gauge theories, including applications to experimental physics.

## Key findings

- Constraints on nonlinear Lorentz violation from photon-photon scattering experiments
- Derived corrections to deep inelastic scattering cross sections due to Lorentz and CPT violation
- Framework for gauge-invariant Lorentz-violating operators in nonabelian gauge theories

## Abstract

The classification of Lorentz- and CPT-violating operators in nonabelian gauge field theories is performed. We construct all gauge-invariant terms describing propagation and interaction in the action for fermions and gauge fields. Restrictions to the abelian, Lorentz-invariant, and isotropic limits are presented. We provide two illustrative applications of the results to quantum electrodynamics and quantum chromodynamics. First constraints on nonlinear Lorentz-violating effects in electrodynamics are obtained using data from experiments on photon-photon scattering, and corrections from nonminimal Lorentz and CPT violation to the cross section for deep inelastic scattering are derived.