Shape in an Atom of Space: Exploring quantum geometry phenomenology

TL;DR

This paper introduces a phenomenological model of quantum geometry in loop quantum gravity, showing how combinatorial structures influence observable angular corrections without breaking Lorentz invariance or requiring Planck-scale suppression.

Contribution

It develops a model of angular corrections to flat-space geometries based on combinatorial SU(2) recoupling, linking quantum geometry to potential observations.

Findings

Angular corrections arise from combinatorial SU(2) recoupling.

Effects do not involve Lorentz invariance breaking or Planck suppression.

Potential observational signatures in Bhabha scattering.

Abstract

A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. The physical effects involve neither breaking of local Lorentz invariance nor Planck scale suppression, but rather reply on only the combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example of how the effects might be observationally accessible.