Forces from noncommutative geometry

TL;DR

This paper discusses how Connes' noncommutative geometry framework extends Einstein's general relativity to include fundamental forces like electromagnetism and the weak and strong interactions, highlighting the role of parity violation and the Higgs boson.

Contribution

It introduces a novel derivation of fundamental forces from noncommutative geometry, linking geometric structures to particle physics phenomena.

Findings

Derivation of electromagnetic, weak, and strong forces from noncommutative geometry.

Identification of the Higgs boson as a consequence of gauge symmetry breaking.

Explanation of forces as pseudo forces related to gravity and parity violation.

Abstract

Einstein derived general relativity from Riemannian geometry. Connes extends this derivation to noncommutative geometry and obtains electro-magnetic, weak and strong forces. These are pseudo forces, that accompany the gravitational force just as in Minkowskian geometry the magnetic force accompanies the electric force. The main physical input of Connes' derivation is parity violation. His main output is the Higgs boson which breaks the gauge symmetry spontaneously and gives masses to gauge and Higgs bosons.