Particle Knots in Toric Modular Space

Abstract

The goal of this contribution is to relate quarks to knots or loops in a 6-space CP 3 that then ollapses into a torus in real 3-space P 3 instantaneously after the Big Bang, and massive inflation, when 3 quarks unite to form nucleons. IntroductionKedia et. al. in recent paper [10] investigate knotted structures in hydrodynamic fields such as current-guiding magnetic field lines in a plasma, or vortex lines of classical or quantum fields which arise naturally as excitations that carry helicity that is a measure of the knottedness of the field. In particular their Fig.2g is a trefoil which is our Fig.3 without the quadrupole (that will be seen in Section 2 to collapse into a point) and the color-coding.

Icosahedral Symmetry: A Review

“…The lattice of E 8 is a torus or loop as is the space employed by Sundance Bilson Thompson and Smolin to describe Loop Quantum Gravity [4] which underlines the fundamental importance of the icosahedron and Theta function for the analysis of space itself.Actually equation (15)on quantum gravity incorporates a vibrating surface that could also carry strings. Some time ago Penrose [27] emphasized the relevance of the 5 Platonic solids in physical reality that Plato foresaw 2300 years ago.…”

“…The many nucleon case was found by computing the tensor product [13] instead of postulating a strong force. In particular 15 N was found to exhibit a giant resonance that could be in phase with a low frequency neutrino and a temperature drop of up to 4 degrees C was actually observed in a cylinder of nitrogen at night when only neutrinos could penetrate.…”

“…An infinitesimal time after the Big Bang the 6d Planck space CP 3 is believed to compactify to the projective space P 3 when quarks in Planck space generate nucleons and the τ and µ mesons collapse to the nucleons in Deuterium [15] giving rise to the mass formula discussed in Section 5.From another standpoint masses of the quarks ,W ± bosons and the electron may be related to the number of possibilities or entropy in the algebraic representation (cf.Section 5) …”

Icosahedral Supersymmetry and Dark Matter

“…The paths on the graph of E 8 in the frontispiece of [4] that meet the inner ring of the torus could be gluons as discussed in [9]. Also knots or loops in space may underlie Loop Quantum Gravity according to Sundance Bilson Thompson and Smolin et.al.…”

Icosahedral Supersymmetry

“…Another set of 15 synthemes is considered in [9] on a Knot Theory which describes Fig,1 as a toric knot that could lie in a knotted space which is believed to carry the vortex lines of classical and quantum fields that arise naturally as excitations which carry helicity. In this contribution the inner ring of Fig.1 in the 6-d projective space CP 3 is supposed to compactify to a point at the origin for the e ± , e ν triality, when quarks in the 6-space contract to nucleons in a 3d projective space P 3 which holds 15 synthemes according to Barth and Nieto [2].Twelve synthemes remain on the outer surface of Fig.1 contributed by 6 for the protons and neutrons of equation (3) 1 taken from Coxeter [3,4] shows an arrangement of the 27 lines governed by (su 3 ) 3 .…”