The Elementary Particles as Quantum Knots in Electroweak Theory

Abstract

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 $D_{m{m}^{\prime }}^j$, irreducible representations of $S{U}_q(2)$, 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.

29 pages; LaTex file

Cited by in corpus (9)

• Knots and Preons
• Braided fermions from Hurwitz algebras
• Zitterbewegung structure in electrons and photons
• Quantum groups and braid groups as fundamental symmetries
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
• Charge specific baryon mass relations with deformed SU_q(3) flavor symmetry
• Magnetic moments of octet baryons with deformed Uq(su(3)) flavor symmetry
• Are Dyons the Preons of the Knot Model?
• Knotted boundaries and braid only form of braided belts