Knots and Preons

TL;DR

This paper proposes a model where elementary fermions are composed of preons, which are represented by specific quantum algebra representations, and shows how knot theory can be applied at the preon level to replicate standard particle properties.

Contribution

It introduces a preon-based model using SL_q(2) representations that reproduces the knotted standard theory and links elementary fermions to preon configurations.

Findings

Elementary fermions can be modeled as composite states of preons.

Preons are described by SL_q(2) representations as Lorentz spinors and bosons.

The model suggests particles are indirectly observable through their preon structure.

Abstract

It is shown that the four trefoil solitons that are described by the irreducible representations D^{3/2}_{mm'} of the quantum algebra SL_q(2) (and that may be identified with the four families of elementary fermions (e,\mu,\tau;\nu_e\nu_\mu\nu_\tau;d,s,b;u,c,t) may be built out of three preons, chosen from two charged preons with charges (1/3,-1/3) and two neutral preons. These preons are Lorentz spinors and are described by the D^{1/2}_{mm'} representation of SL_q(2). There are also four bosonic preons described by the D^1_{mm'} and D^0_{00} representations of SL_q(2). The knotted standard theory may be replicated at the preon level and the conjectured particles are in principle indirectly observable.