The $BFCG$ Theory and Canonical Quantization of Gravity

TL;DR

This thesis introduces the $BFCG$ theory, a categorical generalization of the $BF$ model, which is classically equivalent to General Relativity and aims to improve quantum gravity models and their coupling to matter.

Contribution

It presents the $BFCG$ theory as a novel categorical extension of $BF$ models, addressing key issues in quantum gravity and matter coupling.

Findings

Classical equivalence to General Relativity

Potential to improve spinfoam quantum gravity models

Addresses fermion coupling and semiclassical limits

Abstract

This is a PhD thesis on a categorical generalization of the $BF$ model called the $BFCG$ theory. The new theory is equivalent to General Relativity at the classical level but, at the quantum level, seeks to address the problem of the coupling of spinfoams to fermions and, the question of the semiclassical limit of a spinfoam model. Please see enclosed abstract for further details.