Searcharxiv⌕ Search

arXiv subjects

Robert J. Finkelstein

Publications and source records attributed to Robert J. Finkelstein.

25 records · Page 2Linked to original sources
arXiv2005

Masses and Interactions of q-Fermionic Knots

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.

hep-th↗
arXiv2005

A Knot Model Sugugested by the Standard Electroweak Theory

We attempt to go beyond the standard electroweak theory by replacing SU(2) with its q-deformation: SU_q(2). This step introduces new degrees of freedom that we interpret as indicative of non-locality and as a possible basis for a solitonic model of the elementary particles. The solitons are conjectured to be knotted flux tubes labelled by the irreducible representations of SU_q(2), an alglebra which is not only closely related to the standard theory but also plays an underlying role in the description of knots. Each of the four families of elementary fermions is conjectured to be represented by one of the four possible trefoils. The three individual fermions belonging to any family are then assumed to occupy the three lowest states in the excitation spectrum of the local trefoil for that family. One finds a not unreasonable variation of q among the lepton and quark families. The model in its present form predicts a fourth generation of fermions as well as a neutrino mass spectrum. The model may be refined depending on whether or not the fourth generation is found.

hep-th↗
arXiv2003

On q-SU(3) Gauge Theory

We study the replacement of SU(3) by SU_q(3) in standard gauge theories. At the level of a global theory there is a physically sensible SU_q(3) formalism with measurable differences from the SU(3) theory. In contrast to the SU_q(2) case, where it is possible to construct a q-electroweak theory, there is no local (Yang-Mills) formalism for SU_q(3).

hep-th↗
arXiv1997

q-Uncertainty Relations

As one would anticipate from the realization of the q-commutators by difference operators, the states of maximum localization are smeared delta functions depending on q.

q-alg↗
arXiv1995

q-Gauge Theory

We examine some issues that arise in the q-deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields by the corresponding q-commutators, the resulting propagators are not very much different from those of the undeformed theory as long as one is dealing with weak fields; but the theory still violates causality. If one postulates a q-deformed S matrix, the corresponding q-causal commutator has 2 poles of different strength and the result again amounts to a deformation of the Lorentz group.

q-alg↗