Light-Light scattering in Very Special Relativity Quantum Electrodynamics and Cosmic Anisotropies

TL;DR

This paper investigates light-light scattering within Very Special Relativity (VSR) QED, revealing tiny anisotropies in scattering cross sections that could be detectable in cosmic microwave background observations.

Contribution

It demonstrates that VSR QED with a photon mass preserves gauge invariance and unitarity, and shows that the scattering results match standard QED with an effective electron mass.

Findings

One-loop diagrams reduce to standard QED results with effective electron mass.

Total scattering cross section exhibits tiny anisotropies.

Anisotropies could be observed in the Cosmic Microwave Background at low frequencies.

Abstract

We consider scattering of light by light in Very Special Relativity (VSR) Quantum Electrodynamics(QED) with a non-zero photon mass. In order to preserve gauge invariance and Sim(2) symmetry we made use of a recently introduced infrared regularization of VSR theories. Additionally we show that all one loop diagrams with any number of photon external legs and zero fermion legs reduce to the standard QED result with the effective electron mass, as required by unitarity. It follows that the Euler-Heisenberg Lagrangian is the same as in QED. The total cross section of scattering of light by light exhibits tiny anisotropies that could be detected at cosmological scales. In particular they should be looked at the Cosmic Microwave Background(CMB) Radiation for low photon frequencies.