On the possibility of nonlinear de Broglie relations for very-high-energy photons

Fernando Parisio

Published 2019-05-20Version 1

While quantum field theory is at the heart of our understanding of a large variety of phenomena, there remains some discrepancies between theoretically predicted and observed quantities in the very-high-energy (VHE) domain. In this work, starting from commutation relations between phase-space operators (in ``first quantization'') we define averaged creation and annihilation operators and show that they satisfy a simple, deformed commutation relation. By extending this relation to the quantized electromagnetic field, we are led to non-linear de Broglie relations for photons, which appreciably differ from $E=\hbar \omega$ and $\mathbf{p}=\hbar \mathbf{k}$ only in the VHE regime. The nonlinear Compton scattering that follows from these assumptions is discussed. We suggest that this hypothesis may be a way to deal with the pair-production anomaly and show that it may lead to an attenuation in the cosmological-constant problem of several orders of magnitude.