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

R. N. C. Pfeifer

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arXiv · 2108.07719

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

R. N. C. Pfeifer

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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.

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BibTeX RIS

R. N. C. Pfeifer. 2021-08-08. A Classical Analogue to the Standard Model, Chapter 2: Colour interactions and fermions from scalar fields on $\mathbb{C}^{\wedge 6}$. https://arxiv.org/abs/2108.07719

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