# Quanta of Space-Time and Axiomatization of Physics

## TL;DR

This paper proposes a noncommutative geometric framework that quantizes space-time, predicts a unified particle interaction model, and offers insights into fundamental physics including gravity, cosmology, and dark matter.

## Contribution

It introduces a higher degree Heisenberg relation involving the Dirac operator, leading to a noncommutative space that unifies particle physics and gravity.

## Key findings

- Volume quantization emerges from the commutation relation.
- The model predicts a unified structure of particle interactions.
- Implications for cosmology and dark matter are discussed.

## Abstract

We consider Hilbert's sixth problem on the axiomatization of physics starting with a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. The two sided version of the commutation relation in dimension 4 implies volume quantization and determines a noncommutative space which is a tensor product of continuous and discrete spaces. This noncommutative space predicts the full structure of a unified model of all particle interactions based on Pati-Salam symmetries or, as a special case, the Standard Model. We study implications of this quantization condition on Particle Physics, General Relativity, the cosmological constant and dark matter. We demonstrate that, with little input, noncommutative geometry gives a compelling and attractive picture about the nature and structure of space-time.