The Elementary Particles as Quantum Knots in Electroweak Theory

TL;DR

This paper proposes a novel model where elementary particles are represented as quantum knots within an electroweak framework, linking knot topology to particle quantum numbers and interactions.

Contribution

It introduces a knot-based quantum model of elementary particles compatible with electroweak theory, relating knot invariants to standard quantum numbers and describing particle interactions as knot emissions.

Findings

Elementary fermions as quantum trefoils (N=3)

Gauge bosons as ditrefoils (N=6)

Modified electroweak Lagrangian consistent with knot model

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 $D^j_{mm'}$, 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.