Masses and Interactions of q-Fermionic Knots

Details Masses and Interactions of q-Fermionic Knots Masses and Interactions of q-Fermionic Knots

2005-07-01

arxiv.org/abs/hep-th/0507022v2

Int.J.Mod.Phys.A21:4269-4302,2006

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, 2 figures, latex format

Scientific paper

10.1142/S0217751X06032496

The q-electroweak theory suggests a description of elementary particles as solitons labelled by the irreducible representations of SU_q(2). Since knots may also be labelled by the irreducible representations of SU_q(2), we study a model of elementary particles based on a one-to-one correspondence between the four families of Fermions (leptons, neutrinos, (-1/3) quarks, (2/3) quarks) and the four simplest knots (trefoils). In this model the three particles of each family are identified with the ground and first two excited states of their common trefoil. Guided by the standard electroweak theory we calculate conditions restricting the masses of the fermions and the interactions between them. In its present form the model predicts a fourth generation of fermions as well as a neutrino spectrum. The same model with q almost equal to 1 is compatible with the Kobayashi-Maskawa matrix. Depending on the test of these predictions, the model may be refined.

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