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

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.