Categorical generalization of spinfoam models

TL;DR

This paper reviews quantum gravity challenges, discusses spinfoam models in Loop Quantum Gravity, and introduces category theory to improve their semiclassical limit and matter coupling.

Contribution

It proposes a new categorical formalism for spinfoam models, addressing key issues in semiclassical behavior and matter field coupling.

Findings

New categorical formalism for spinfoam models

Improved semiclassical limit in quantum gravity models

Enhanced matter coupling in covariant quantization

Abstract

We give a brief review of the problem of quantum gravity. After the discussion of the nonrenormalizability of general relativity, we briefly mention the main research directions which aim to resolve this problem. Our attention then focuses on the approach of Loop Quantum Gravity, specifically spinfoam models. These models have some issues concerning the semiclassical limit and coupling of matter fields. The recent developments in category theory provide us with the necessary formalism to introduce a new action for general relativity and perform covariant quantization so that the issues of spinfoam models are successfully resolved.