Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-05-24
Int.J.Mod.Phys.A22:4467-4480,2007
Physics
High Energy Physics
High Energy Physics - Theory
29 pages; LaTex file
Scientific paper
10.1142/S0217751X0703707X
We explore a knot model of the elementary particles that is compatible with electroweak physics. The knots are quantized and their kinematic states are labelled by $D^j_{mm'}$, 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 $(t,t_3,t_0)$ by $(t=N/6,t_3=-w/6,t_0=-(r+1)/6)$, where $t_0$ 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. In this framework we have explored a slightly modified standard electroweak Lagrangian with a slightly modified gauge group which agrees closely but not entirely with standard electroweak theory.
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