Could the photon dispersion relation be non-linear ?

TL;DR

This paper explores the possibility of non-linear photon dispersion relations as a test of Lorentz Invariance Violation, analyzing theoretical models and phenomenological implications, especially in cosmic ray propagation and non-commutative space theories.

Contribution

It provides a non-perturbative analysis of the photon dispersion relation within non-commutative space field theory, offering new insights into potential LIV signatures.

Findings

Non-perturbative results for NC photon dispersion relation

Potential LIV signals in cosmic ray and GRB observations

Theoretical framework linking non-commutative geometry to photon dispersion

Abstract

The free photon dispersion relation is a reference quantity for high precision tests of Lorentz Invariance. We first outline theoretical approaches to a conceivable Lorentz Invariance Violation (LIV). Next we address phenomenological tests based on the propagation of cosmic rays, in particular in Gamma Ray Bursts (GRBs). As a specific concept, which could imply LIV, we then focus on field theory in a non-commutative (NC) space, and we present non-perturbative results for the dispersion relation of the NC photon.