2-categorical Poincare Representations and State Sum Applications

TL;DR

This paper introduces a new 2-categorical representation theory framework for Poincare symmetries, aiming to develop a state sum model for 4D Quantum Gravity, highlighting its rich structure and geometric quantization connections.

Contribution

It develops a novel representation 2-category for Lie 2-group symmetries tailored to 4D Quantum Gravity models, extending geometric quantization to a categorified setting.

Findings

Rich structure reflecting 4-dimensional physical characteristics

Framework suitable for state sum models in Quantum Gravity

Categorification of geometric quantization methods

Abstract

This is intended as a self-contained introduction to the representation theory developed in order to create a Poincare 2-category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation 2-category appropriate to Lie 2-group symmetries and discuss its application to the problem of finding a state sum model for Quantum Gravity. There is a remarkable richness in its details, reflecting some desirable characteristics of physical 4-dimensionality. We begin with a review of the method of orbits in Geometric Quantization, as an aid to the intuition that the geometric picture unfolded here may be seen as a categorification of this process.