Scattering Cross-Sections in Quantum Gravity - the Case of Matter-Matter Scattering

TL;DR

This paper develops a gauge theory of volume-preserving diffeomorphisms for quantum gravity, calculates matter-matter scattering cross-sections, and confirms consistency with Newtonian gravity in the non-relativistic limit.

Contribution

It introduces a gauge theory framework for quantum gravity based on volume-preserving diffeomorphisms and derives scattering cross-sections within this model.

Findings

Derived the S-matrix element for matter scattering in the gauge theory.

Calculated the scattering cross-section to leading order in perturbation theory.

Recovered the Rutherford-like scattering cross-section in the non-relativistic limit.

Abstract

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of a four-dimensional in- ner space. To analyse scattering in this theory the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity