A Classical Analogue to the Standard Model, Chapter 2: Colour interactions and fermions from scalar fields on $\mathbb{C}^{\wedge 6}$

Abstract

This paper continues the study of quasiparticles on complex manifolds with anticommuting co-ordinates, and shows that on increasing the dimensionality of the complex manifold from $\mathbb{C}^{\wedge 2}$ to $\mathbb{C}^{\wedge 6}$, the dimension-$L^{-1/2}$ spinor excitations in the associated effective field theory on $\mathbb{R}^{1,3}$ acquire an $\mathrm{SU}(3)$ colour charge and assemble into composite spinors of dimension $L^{-3/2}$. This model provides a novel environment in which to study colour confinement, while also demonstrating the ability of the first member of the $\mathbb{C}^{\wedge 6\mathfrak{n}}$ series to support fermions having spin and dimensions consistent with the Standard Model.