THE ELEMENTARY PARTICLES AS QUANTUM KNOTS IN ELECTROWEAK THEORY
Robert J. Finkelstein · International Journal of Modern Physics A · 2007
We explore a knot model of the elementary particles that is compatible with electroweak physics. The knots are quantized and their kinematic states are labeled by [Formula: see text], irreducible representations of SU q(2), where j = N/2, m = w/2, m′ = (r+1)/2 and (N, w, r) designate respectively the number of crossings, the writhe, and the rotation of the knot. The knot quantum numbers (N, w, r) are related to the standard isotopic spin quantum numbers (t, t3, t0) by (t = N/6, t3 = -w/6, t0 = -(r+1)/6), where t0 is the hypercharge. In this model the elementary fermions are low lying states of the quantum trefoil (N = 3) and the gauge bosons are ditrefoils (N = 6). The fermionic knots interact by the emission and absorption of bosonic knots.