- #476

CarlB

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Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation

Piotr Zenczykowski.

According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.

http://arxiv.org/abs/0901.2896

So does the above have anything to do with the way Garrett packs a single generation into E8? I don't think so but others understand his theory better than me.

P.S.

MTd2, when I had done this originally, it was based on assumptions which violated special relativity. That probably put Smolin off his feed. The latest version hides all that stuff by sticking to quantum information theory (where position and momentum are ignored, hence there is no need for special relativity or a replacement for it) and so that might get by better.

I seem to have given it an attractive abstract because some important people have written to me saying that they are very busy, especially this time of year, but they are going to take the time to read the paper. I think that basically, it's an attractive way of extending Regge trajectories to radial excitations and I wonder if I should give it a title that mentions Regge trajectories instead of Koide mass formulas. Hmmm.