Background independent quantization and wave propagation

TL;DR

This paper explores a background independent quantization method applied to a scalar field, revealing nonlinear, Lorentz-violating wave equations with amplitude-dependent dispersion relations, and discusses potential experimental detection.

Contribution

It introduces a novel polymer quantization approach for scalar fields, deriving amplitude-dependent dispersion relations and analyzing their physical implications.

Findings

Polymer corrections depend on wave amplitude.

Dispersion relations vary with wave shape and frequency.

Polymer effects accumulate over time in wave propagation.

Abstract

We apply a type of background independent "polymer" quantization to a free scalar field in a flat spacetime. Using semi-classical states, we find an effective wave equation that is both nonlinear and Lorentz invariance violating. We solve this equation perturbatively for several cases of physical interest, and show that polymer corrections to solutions of the Klein-Gordon equation depend on the amplitude of the field. This leads to an effective dispersion relation that depends on the amplitude, frequency and shape of the wave-packet, and is hence distinct from other modified dispersion relations found in the literature. We also demonstrate that polymer effects tend to accumulate with time for plane-symmetric waveforms. We conclude by discussing the possibility of measuring deviations from the Klein-Gordon equation in particle accelerators or astrophysical observations.