On Particles and Primes
Abstract
Primes in the two complete associative normed division algebras C and H have affinities with structures seen in the standard model of particle physics. On the integers in the two algebras, there are two equivalence relations: a strong one, related to a U(1) and SU(3) symmetry allowing to permute and switch signs of the coordinates of the integers, as well as a weak relation with origins from units U(1),SU(2) in the algebra. Weak equivalence classes within the strong equivalence classes of odd primes in C case relate to leptons, the inert ones being neutrino like, and the split ones resembling electron-positron pairs. In the H case, for odd primes, the equivalence classes come in groups of two or three, leading to a caricature of hadrons featuring either mesons built by a quark pair or then baryons obtained by quark triplets. We can now list for every rational prime p all these particles and attach fractional charges to its constituents.
Cite
@article{arxiv.1608.07175,
title = {On Particles and Primes},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:1608.07175},
year = {2016}
}
Comments
39 pages, 14 figures. arXiv admin note: text overlap with arXiv:1606.05971