Non-commutative fermion mass matrix and gravity

TL;DR

This paper explores algebraic methods in non-perturbative quantum gravity, introduces a new algebraic characterization of the Dirac operator in non-commutative geometry, and discusses implications for the fermion mass matrix and quantum spectral gravity.

Contribution

It presents a novel algebraic characterization of the Dirac operator and applies it to analyze the fermion mass matrix within non-commutative geometry, advancing understanding of quantum spectral gravity.

Findings

New algebraic characterization of the Dirac operator

Application to fermion mass matrix analysis

Speculative perspective on quantum spectral gravity

Abstract

The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of the nature of geometry. This helps to set the context for the second part, in which we describe a new algebraic characterisation of the Dirac operator in non-commutative geometry and then use it in a calculation on the form of the fermion mass matrix. Assimilating and building on the various ideas described in the first part, the final part consists of an outline of a speculative perspective on (non-commutative) quantum spectral gravity. This is the second of a pair of papers so far on this project.