Towards an axiomatic model of fundamental interactions at Planck scale

TL;DR

This paper proposes an axiomatic framework using noncommutative geometries to unify all four fundamental interactions and describe sub-atomic particle properties and behaviors at the Planck scale.

Contribution

It introduces a novel axiomatic model that encodes particle formation, interactions, and symmetries within a noncommutative geometric setting.

Findings

Unified description of fundamental interactions

Encoding of particle properties and symmetries

Potential framework for quantum gravity theories

Abstract

By exploring possible physical sense of notions, structures, and logic in a class of noncommutative geometries, we try to unify the four fundamental interactions within an axiomatic quantum picture. We identify the objects and algebraic operations which could properly encode the formation and structure of sub-atomic particles, antimatter, annihilation, CP-symmetry violation, mass endowment mechanism, three lepton-neutrino matchings, spin, helicity and chirality, electric charge and electromagnetism, as well as the weak and strong interaction between particles, admissible transition mechanisms (e.g., muon to muon neutrino, electron, and electron antineutrino), and decays (e.g., neutron to proton, electron, and electron antineutrino).