Unified model of loop quantum gravity and matter

TL;DR

This paper revisits a unified model of gravity and matter within loop quantum gravity, demonstrating a consistent Euclidean quantization and discussing challenges in the Lorentzian case.

Contribution

It shows how to promote the Hamiltonian constraint to an anomaly-free quantum operator in the Euclidean theory, advancing the quantization of unified gravity-matter models.

Findings

Euclidean model can be quantized anomaly-free using Thiemann's techniques

Lorentzian model construction is consistent but faces quantization challenges

Weak field limit of Lorentzian model is only correct under restrictive assumptions

Abstract

We reconsider the unified model of gravitation and Yang--Mills interactions proposed by Chakraborty and Peld\'an, in the light of recent formal developments in loop quantum gravity. In particular, we show that one can promote the Hamiltonian constraint of the unified model to a well defined anomaly-free quantum operator using the techniques introduced by Thiemann, at least for the Euclidean theory. The Lorentzian version of the model can be consistently constructed, but at the moment appears to yield a correct weak field theory only under restrictive assumptions, and its quantization appears problematic.