Dimensional Reduction

TL;DR

This paper introduces a novel dimensional reduction mechanism using octonionic formalism that naturally yields three particle generations with realistic spectra from a 10-dimensional spacetime without compactification.

Contribution

The work presents a new approach to dimensional reduction employing octonions, resulting in a particle spectrum matching three generations of leptons directly from a 10D Dirac equation.

Findings

Achieves dimensional reduction without compactification.

Produces exactly three particle generations with realistic spectra.

Identifies implications for spacetime structure and curved backgrounds.

Abstract

Using an octonionic formalism, we introduce a new mechanism for reducing 10 spacetime dimensions to 4 without compactification. Applying this mechanism to the free, 10-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly 3 generations. Each generation contains 1 massive spin-1/2 particle with 2 spin states, 1 massless spin-1/2 particle with only 1 helicity state, and their antiparticles --- precisely one generation of leptons. There is also a single massless spin-1/2 particle/antiparticle pair with the opposite helicity and no generation structure. We conclude with a discussion of some further consequences of this approach, including those which could arise when using the formalism on a curved spacetime background, as well as the implications for the nature of spacetime itself.