Knots and Preons

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,μ,τ;ν_eν_μν_τ;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.

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