Causal sites as quantum geometry

TL;DR

The paper introduces causal sites as a novel framework for quantum geometry, replacing point sets with a categorical structure that can approximate classical gravity solutions and supports quantization.

Contribution

It proposes causal sites as a new categorical structure for quantum geometry, including a tangent 2-bundle and an approach to quantization.

Findings

Causal sites have an intrinsic geometry approximating classical general relativity.

The structure has a natural tangent 2-bundle analogous to smooth manifolds.

An initial approach to quantizing causal sites is proposed.

Abstract

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relativity. We propose an approach to quantization of causal sites as well.