2016/08/22 by Oliver Knill, Knill, Oliver · 1 citation
Mathematics · Physics and Astronomy · #11A99 #11R52 #11Z99 #17A35 #20G20 #Algebraic and Geometric Analysis #FOS: Physical sciences #Finite Group Theory Research #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1608.07175
openalex publication_date 2016/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.