The Photon Dispersion as an Indicator for New Physics ?

We first comment on the search for a deviation from the linear photon dispersion relation, in particular based on cosmic photons from Gamma Ray Bursts. Then we consider the non-commutative space as a theoretical concept that could lead to such a deviation, which would be a manifestation of Lorentz Invariance Violation. In particular we review a numerical study of pure U(1) gauge theory in a 4d non-commutative space. Starting from a finite lattice, we explore the phase diagram and the extrapolation to the continuum and infinite volume. These simultaneous limits - taken at fixed non-commutativity - lead to a phase of broken Poincare symmetry, where the photon appears to be IR stable, despite a negative IR divergence to one loop.

💡 Research Summary

The paper tackles the possibility that deviations from the linear photon dispersion relation—ω = c |k|—might signal new physics, focusing on two complementary approaches: observational constraints from high‑energy astrophysical photons and a theoretical model based on non‑commutative (NC) geometry. In the first part the authors review the status of time‑of‑flight measurements from gamma‑ray bursts (GRBs). By comparing the arrival times of photons with widely separated energies, one can bound any energy‑dependent speed of light. Current data, especially from short, bright bursts such as GRB 090510, constrain the relative variation Δc/c to the order of 10⁻¹⁶, leaving only a narrow window for Planck‑scale effects. The authors stress that while these limits are extremely stringent, they do not completely rule out a tiny, sub‑Planckian modification that could become visible with next‑generation detectors.

The second, more technical part of the work investigates a pure U(1) gauge theory formulated on a four‑dimensional Euclidean lattice endowed with a Moyal star product, which implements the canonical non‑commutative relation