A Classical Analogue to the Standard Model, Chapter 3: Standard Model particle spectrum from scalar fields on $\mathbb{C}^{\wedge 18}$

TL;DR

This paper constructs a mathematical model using scalar fields on a complex Grassmann manifold that replicates the Standard Model particle spectrum, including additional bosons and gluons, providing a novel analogue framework.

Contribution

It introduces the $ ext{C}^{ ext{wedge} 18}$ model as the smallest Grassmannian-based analogue capable of mimicking the Standard Model particle spectrum.

Findings

Particle spectrum resembles Standard Model plus extra bosons

Includes a ninth gluon not in the Standard Model

Model fixed gauge degrees of freedom to match known particles

Abstract

The $\mathbb{C}^{\wedge 2\mathfrak{n}}$ models are analogue models which generate Lagrangians for quasiparticles on $\mathbb{R}^{1,3}$ from antisymmetric vector products on Grassmann manifolds. This paper introduces $\mathbb{C}^{\wedge 18}$, the smallest member of this series which is capable of hosting a quasiparticle spectrum analogous to the Standard Model. Once all gaugeable degrees of freedom have been fixed, the particle spectrum of $\mathbb{C}^{\wedge 18}$ is seen to resemble the Standard Model plus two additional weakly interacting bosons and a ninth gluon.