Photon frequency variation in non-linear electro-magnetism

TL;DR

This paper explores how a generalized non-linear electromagnetic Lagrangian predicts photon frequency shifts in space-time dependent backgrounds, revealing new effects like energy variation and potential cosmological implications.

Contribution

It introduces the first analysis of photon energy variation and frequency shifts in non-linear electromagnetism, extending beyond classical Maxwell theory.

Findings

Photon energy varies in space-time dependent backgrounds.

Photon frequency experiences red or blue shifts in non-linear theories.

Potential implications for cosmology and atomic spectra.

Abstract

We set a generalised non-linear Lagrangian, encompassing Born-Infeld and Heisenberg-Euler theories among others. The Lagrangian reduces to the Maxwell Lagrangian at lowest order. The field is composed by a propagating light-wave in an electro-magnetic background. The wave exhibits energy variation when the background is space-time dependent. In the photon description, this implies a red or a blue shift, like what we obtained in massive theories, as the de Broglie-Proca or effective mass theories as the Standard-Model Extension under Lorentz symmetry violation. The two results, photon energy-conservation and the frequency shift are instead new for non-linear electro-magnetism. We conclude by discussing how these static frequency shifts when added to the expansion red shift allow new interpretations in cosmology or for atomic spectra. We finally consider the consequences on the Poincar\'e symmetry.