Families Of Elementary Particles Research Articles

Braids as a representation space of SU(5)

The standard model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary is still unknown. Along the lines of previous preon models positing a substructure to explain these aspects, Bilson-Thompson showed how the first family of elementary particles is realized as the crossings of braids made of three strands, with charges resulting from twists of those strands with certain conditions; in this topological model, there are only two distinct neutrino states. Modeling the particles as braids implies these braids must be the representation space of a Lie algebra, giving the symmetries of the standard model. In this paper, this representation is made explicit, obtaining the raising operators associated with the Lie algebra of SU(5), one of the earliest grand unified theories. Because the braids form a group, the action of these operators are braids themselves, leading to their identification as gauge bosons. Possible choices for the other two families are also given. Although this realization of particles as braids is lacking a dynamical framework, it is very suggestive, especially when considered as a natural method of adding matter to loop quantum gravity.

Generalized Dirac and Klein-Gordon equations for spinor wavefunctions

A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equa- tion for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon equations are also derived. In the non-relativistic limit the generalized Dirac equation gives the general- ized Levy-Leblond equation and the generalized Pauli-Schrodinger equa- tion. The main difference between the original and generalized Dirac equations is that the former and latter are obtained with zero and non- zero phase functions, respectively. Otherwise, both equations describe free elementary particles with spin 1/2, which have all other physical properties the same except their masses. The fact that the generalized Dirac equation describes elementary particles with larger masses is used to suggest that non-zero phase functions may account for the existence of three families of elementary particles in the Standard Model. This suggestion significantly differs from those previously made to account for the three families of particle physics.

A classical path to unification

An overview is given of a classical unified theory of gravity, elementary particles and quantum phenomena based on soliton solutions of Einstein's vacuum equations in twelve dimensional space. Bell's theorem on the Einstein-Podolsky-Rosen experiment, which is widely interpreted as ruling out classical explanations of quantum phenomena, is shown to be non-applicable as violating time-reversal symmetry. Entanglement is a relativistic consequence of Newon's third law and a property of all time-symmetrical theories, whether classical or quantal. The metric solitons (metrons) are composed of strongly nonlinear periodic core components, far fields corresponding to the classical gravitational and electromagnetic far fields of point-like particles, and further fields representing the weak and strong interactions. The core fields represent nonlinear eigenmodes trapped in a self-generated wave guide. Computations are presented for the first family of elementary particles corresponding to the lowest nonlinear eigenmodes; the second and third families are assumed to correspond to higher eigenmodes. It is shown that the periodicities of the soliton core modes produce the wave-particle duality paradoxes of quantum phenomena, as exemplified by single- and double-slit particle diffraction and the discrete structure of atomic spectra.

Generalized Levy-Leblond and Schrodinger equations for spinor wavefunctions

New fundamental (Galilean invariant) dynamical equations for four- component spinor wavefunctions are derived by using a different phase function than the Schrodinger phase function. The derived equations are called the generalized Levy-Leblond and generalized Schrodinger equa- tions because these equations reduce to the standard Levy-Leblond and Schrodinger equations when the Schrodinger phase function is used. The generalized and standard equations describe the same free elementary particles with spin 1/2, however, masses of the particles described by these equations are not the same as the generalized equations automati- cally account for particles with larger masses. This has important phys- ical implications as it shows that elementary particles with the same physical properties but different masses can result from using phase functions different than the Schrodinger phase function. Therefore, the main conclusion of this paper is that the existence of the three currently known families of elementary particles in the Standard Model of particle physics can be theoretically accounted for by choosing different phase functions.

EXTENDED PARTICLE MODELS BASED ON HOLLOW SINGULAR HYPERSURFACES IN GENERAL RELATIVITY: CLASSICAL AND QUANTUM ASPECTS OF CHARGED TEXTURES

In the present paper we construct classical and quantum models of an extended charged particle. One shows that consecutive modelling can be based on the hollow thin-wall charged texture which acquires gravitational mass due to Einstein–Maxwell interaction. We demonstrate that such a model has equilibrium states at the radius equal to the established classical radius of a charged particle. Also we consider quantum aspects of the theory and obtain the Dirac sea conception in a natural way. Besides, the phenomenological unification on the mass level of the two families of elementary particles, charged pions and electrons and positrons, evidently arises as the effect induced by classical and quantum gravity prior to Standard Model.

Earthquake Jostles the New Stanford Linear Collider

On 12 October the Stanford Linear Accelerator Center announced its finding that Nature has only three families of elementary particles.’ (See PHYSICS TODAY, October, page 17) Five days later, as if in anger at having its secret revealed, Nature shook the offending instrument—the recently completed Stanford Linear Collider—by the throat. All things considered, the SLC has suffered relatively little damage from the historic earthquake that struck the San Francisco Bay area at 5:04 pm on 17 October. Still, the small misalignments caused by the quake have interrupted the physics schedule of the collider for more than a month. As of this writing, the fond expectation at SLAC is for “a few more Z°'s by Christmas.”

Investigation of the invariance group in the three fundamental fields model

For a theory in which elementary particles are represented by products of fundamental fields, consequences of an invariance group are investigated. The invariance group is the three-by-three unitary group. Tensor-calculus is used to investigate the representations, quantum numbers are defined and it is tried to identify certain families of elementary particles with irreducible representations.

The Rutherford Memorial Lecture, 1958

Five years ago in this University Sir James Chadwick gave the second Rutherford Memorial Lecture. I have read it many times and find it an admirable account of Rutherford’s scientific career and a wise and understanding description of his outstanding genius as an experimental physicist. Chadwick gave special emphasis to Rutherford’s remarkable achievements during his tenure of the MacDonald Chair of Physics here at McGill and to the great debt that the world of science owes to this University in giving such excellent facilities to such a young man. Together with the four other Memorial Lectures given under the auspices of the Royal Society, a very complete account has been given of Rutherford’s life and achievements. I will not attempt to recapitulate the story, but will content myself with a commentary on certain aspects of Rutherford’s attitude to the art of the experimenter which seem to be of special interest today. Here in McGill the exponential decay with time of radioactive substances was first observed and interpreted as being due to spontaneous disintegration of an atom. A quarter of a century elapsed before this brilliant phenomenological interpretation by Rutherford and Soddy was to receive a theoretical explanation in terms of wave mechanics. Today, with the surprising developments of the last decade and the discovery of whole families of unstable elementary particles, we now see that the spontaneous decay of one subatomic bit of matter into lighter pieces is one of the most significant facts of the subatomic world. In point of fact, these families of elementary particles are superficially not unlike the families of radioactive elements which Rutherford and his co-workers did so much to disentangle. An outstanding difference is, of course, that no one has found a theoretical explanation of the spontaneous decay of elementary particles and most theorists believe that none is to be sought, but that such behaviour is just a fundamental property of microscopic matter.

International Conference on the Quantum Interactions of the Free Electron: A Summary Report

The electron has been a bona fide member of the family of elementary particles for over a half of a century and a great deal is now known about its properties. As is usual in scientific endeavor, the more one learns about something the more one finds further questions which need to be answered. The International Conference on the Quantum Interactions of the Free Electron served somewhat as a pause to recapitulate what has been learned and understood and to reformulate the pertinent questions that we would like to have answered.