Reassessing aspects of the photon's LQG-modified dispersion relations
P. A. L. Mourão, G. L. L. W. Levy, J. A. Helayël-Neto
TL;DR
The paper investigates Loop Quantum Gravity effects in the electromagnetic sector by formulating a post-Maxwellian theory with higher-derivative and nonlinear terms, deriving corrected energy-momentum quantities and a modified, anisotropic photon dispersion. It analyzes how a homogeneous background field and linearization yield a dispersion relation that permits vacuum birefringence and altered group velocities, and reexamines Compton kinematics under these corrections, finding a small LQG contribution to the wavelength shift that scales with the Planck length and photon wavelength. The work highlights the potential observational consequences for high-energy astrophysical signals and outlines future directions to constrain LQG parameters via collider and electroweak processes, aiming to connect quantum gravity phenomenology with measurable optical and scattering phenomena.
Abstract
Our present contribution sets out to investigate a scenario based on the effects of the Loop Quantum Gravity (LQG) on the electromagnetic sector of the Standard Model of Fundamental Interactions and Particle Physics (SM). Starting then from a post-Maxwellian version of Electromagnetism that includes LQG effects, we work out and discuss the influence of LQG parameters on classical quantities, such as the components of the stress-tensor. Furthermore, we inspect the propagation of electromagnetic waves and study optical properties of the QED vacuum in this scenario. Among these, we contemplate the combined effect between the LQG parameters and a homogeneous background magnetic field on the propagation of electromagnetic waves, considering in detail issues like group velocities and refractive indices of the QED vacuum. Finally, with the help of the LQG-extended photonic dispersion relations previously analyzed, we re-discuss the kinematics of the Compton effect and conclude that there emerges an interesting nonlinear profile in the wavelengths of both the incoming and the deflected photons.