Poincare 2-group and quantum gravity

TL;DR

This paper reformulates General Relativity as a constrained topological theory using Poincaré 2-group, introduces a novel path-integral quantization approach with edge lengths as variables, and proposes a new 3-complex amplitude for Euclidean quantum gravity.

Contribution

It presents a new formulation of gravity via Poincaré 2-group and develops a path-integral quantization with edge lengths as fundamental variables.

Findings

Gravity formulated as constrained topological theory

Edge lengths emerge as basic variables in quantization

Proposed a new 3-complex amplitude for Euclidean quantum gravity

Abstract

We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge lengths of the spacetime manifold triangulation arise as the basic variables in the path-integral quantization, while the state-sum amplitude is an evaluation of a colored 3-complex, in agreement with the category theory results. A 3-complex amplitude for Euclidean quantum gravity is proposed.