Fuzzy operators and the quantized electromagnetic field in the very-high-energy regime

TL;DR

This paper introduces a novel approach to the quantized electromagnetic field at very-high energies, proposing deformed commutation relations and a new vacuum state that could impact understanding of high-energy photon behavior and cosmological phenomena.

Contribution

It develops a framework with deformed commutation relations for the electromagnetic field and introduces a new vacuum state, leading to nonlinear photon relations and potential cosmological implications.

Findings

Nonlinear de Broglie relations for high-energy photons

A new vacuum state with non-zero components in standard states

Potential attenuation effects relevant to cosmological constant problem

Abstract

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 determine the new vacuum state which has a non-zero component in standard occupied states. In addition we are led to non-linear de Broglie relations for photons, which appreciably depart from linearity only in the very-high-energy 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 transparency of the electromagnetic background light (EBL) and show that it may lead to an attenuation in the cosmological-constant problem of several orders of magnitude.