Hadron Structure of Quaternion Primes
Related to the quaternion integers, which produce the densest known lattice packing in R^4 is a curious relation between number theory and particle physics which I looked at in 2016. It deals with
the question whether the standard model of paraticles is "natural":
--- Leptons:
There is exactly one complete commutative, associative real division algebra: the complex numbers. Their primes show a Lepton structure. Odd primes come in two flavors: the 4k+1 primes, which are bosons as they are composed in the complex by two particles a+ib, a-ib (electron and positron). Then there are the 4k+3 primes which are real and fermions (neutrini).
--- Hadrons:
There is exactly one complete non-Abelian associative real division algebra: the quaternions. Their primes show a Hadron structure. The quaternion integers I carry two symmetry groups. The first is the group U of units, which is the binary ternary group 2T. Then there is the group V generated by coordinate permutations and conjugation. The quotient Q=I/V are the quarks. Why? Because the Q/U equivalence classes either have 2 or 3 elements. The triplets are Baryons, the tuplets are the Mesons. --- References:
https://arxiv.org/abs/1608.07175. Particles and Primes (2016)
https://arxiv.org/abs/1606.05971. Experiments in Number theory (2016)
https://www.quantumcalculus.org/hadro... Mathematica code
This is a "super dangerous topic" as it is in an in the collision of two crackpot indices:
https://math.ucr.edu/home/baez/crackp.... Crackpot index of John Baez
https://t5k.org/notes/crackpot.html Crackpot index of Chris Caldwell
The entry and exit videos were shot two days earlier on the Mystic River in Medford (MA).