Hamiltonian analysis of the BFCG formulation of General Relativity

TL;DR

This paper conducts a comprehensive Hamiltonian analysis of the BFCG formulation of General Relativity, clarifying its constraints and connection to other formulations, and exploring its implications for quantum gravity models.

Contribution

It provides the first complete Hamiltonian analysis of the BFCG action, classifies all constraints, and links it to Einstein-Cartan and triad formulations, advancing quantum gravity research.

Findings

All constraints of the BFCG formulation are identified and classified.

The canonical formulation reduces to Einstein-Cartan and triad formulations.

Introduces a 2-connection suitable for spin-foam basis construction.

Abstract

We perform the complete Hamiltonian analysis of the BFCG action for General Relativity. We determine all the constraints of the theory and classify them into the first-class and the second-class constraints. We also show how the canonical formulation of BFCG General Relativity reduces to the Einstein-Cartan and triad canonical formulations. The reduced phase space analysis also gives a 2-connection which is suitable for the construction of a spin-foam basis which will be a categorical generalization of the spin-network basis from Loop Quantum Gravity.