MASSES AND INTERACTIONS OF q-FERMIONIC KNOTS

Abstract

The q-electroweak theory suggests a description of elementary particles as solitons labeled by the irreducible representations of SU q(2). Since knots may also be labeled 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 ≅ 1 is compatible with the Kobayashi–Maskawa matrix. Depending on the test of these predictions, the model may be refined.