Quanta of Geometry and Unification

TL;DR

This paper demonstrates that space-time volume quantization leads to a noncommutative geometric framework that naturally incorporates Pati-Salam grand unification, with the Standard Model as a special case satisfying specific mathematical constraints.

Contribution

It introduces a novel link between space-time volume quantization and noncommutative geometry, deriving grand unified models from fundamental geometric principles.

Findings

Volume quantization uniquely determines noncommutative geometry

The geometry leads to Pati-Salam grand unified models

Standard Model emerges as a special case satisfying an order one condition

Abstract

This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.