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.Comment: 40 pages, 2 figures, latex forma
