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

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.