Quantization of four-dimensional Abelian gravity

TL;DR

This paper introduces an abelian version of 4D gravity, performs canonical analysis, and quantizes it to obtain an abelian BF theory, providing a simplified model for quantum gravity.

Contribution

It presents a novel abelian formulation of 4D gravity and its quantization, connecting it to abelian BF theory, which simplifies the complex non-abelian case.

Findings

Canonical analysis reveals similarities to Husain-Kuchar gravity

Quantization yields an abelian BF theory

Provides a new simplified model for quantum gravity

Abstract

An abelian version of standard general relativity in the Cartan-Palatini gauge-like formulation in four dimensions has been introduced. Traditional canonical analysis utilizing similarities to the akin Husain-Kuchar SU(2) version of gravity has been performed. The model has been next quantized in the canonical path-integral Faddeev-Popov formalism yielding abelian BF theory.