On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance

TL;DR

This paper develops a simple model to compute modified dispersion relations from loop quantum gravity, compares quantization choices, and discusses potential Lorentz symmetry violations and their dependence on approximation methods.

Contribution

It introduces a straightforward model for loop quantum gravity phenomenology, analyzing effects of different quantizations and the impact on Lorentz invariance within semiclassical approximations.

Findings

Agreement with semiclassical techniques at a quantitative level

Lorentz symmetry violations may be artifacts of approximation schemes

Different quantization choices affect correction orders

Abstract

A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A comparison with more involved semiclassical techniques shows that there is agreement even at a quantitative level. Furthermore, by contrasting Hamiltonian and Lagrangian descriptions we show that possible Lorentz symmetry violations may be blurred as an artifact of the approximation scheme. Whether this is the case in a purely Hamiltonian analysis can be resolved by an improvement in the effective semiclassical analysis.