KNOTS AND PREONS

Abstract

It is shown that the four quantum trefoil solitons that are described by the irreducible representations [Formula: see text] of the quantum algebra SL q(2) [and that may be identified with the four families of elementary fermions (e, μ, τ; νeνμντ;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 fermions and are described by the [Formula: see text] representation of SL q(2). There are also four bosonic preons described by the [Formula: see text] and [Formula: see text] 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.