1205.1026 (Robert J. Finkelstein)
Robert J. Finkelstein
{\bf Abstract.} We examine a quantum group extension of the standard model. The field operators of the extended theory are obtained by replacing the field operators $\psi$ of the standard theory by ${\psi}$D$^j_{mm'}$, where D$^{j}_{mm'}$ are elements of a representation of the quantum algebra SLq(2), which is also the knot algebra. The D$^j_{mm'}$ lie in this algebra and carry the new degrees of freedom of the field quanta. The D$^j_{mm'}$ are restricted jointly by empirical constraints and by a postulated correspondence with classical knots. The elementary fermions are described by elements of the trefoil (j=3/2) representation and the weak vector bosons by elements of the ditrefoil (j=3) representation. The adjoint (j=1) and fundamental (j=1/2) representations define hypothetical bosonic and fermionic preons. In computing the charge and hypercharge, all particles described by higher representations may be regarded as composed of the fermionic preons. The new Lagrangian, which is invariant under gauge transformations on the SLq(2) algebra, fixes the relative masses of fermions within the same family. It also introduces form factors that modify the electroweak couplings and provide a parametrization of the Cabbibo-Kobayashi-Maskawa matrix. This Lagrangian describes the dynamics of fermions and preons at the electroweak level. It is additionally postulated that the preons carry gluon charge and that the fermions, which are three preon systems, are in agreement with the color assignments of the standard model.
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http://arxiv.org/abs/1205.1026
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