The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation recursive. The recursion mechanism is established via a first order equation which bears some resemblance to Dirac equation. In this paper the author limits the discussion to solutions with constant norm but makes use of 4-dimensional hypercomplex numbers in matrix representation, a concept that is formally introduced in a section devoted to that aspect. The particular solutions that are found exhibit symmetries that can be assigned to spin, electric and color charges of elementary particles, leaving mass as a free parameter. Massless particles can also be assigned to special solutions of the source equation, with the cases of photons, gluons and gravitons clearly identified, together with another massless particle which does not seem to be related to anything detected experimentally. Another section deals with particle dynamics under fields, showing that both gravitational and electrodynamics can be modelled by geodesics of the spaces whose metric tensors result from the recursion mechanism. Finally the author suggests two lines of future work, one deriving fields from densities and currents of masses and charges and the other one aimed at determining particles' masses.
We make use of the well-known properties of spontaneous decays of stationary states of bound systems of elementary particles to support the view that the forces which form these systems propagate instantaneously at the moment of their decay.
Postulating that spacetime is discrete, we assume that physical space is described by a 3-dimensional cubic lattice.The corresponding symmetry group of rotations has order 24 and motivates the introduction of a cubic shaped graph with 27 vertices and 351 edges. We call this graph the elementary particle cube (EPC) and consider the vertices as tiny cells that pre-elementary particles called preons can occupy and the edges as interactions between preons. The 23 nontrivial members of the symmetry group naturally associate with the 23 basic elementary particles. We assume that each elementary part…
Comment on "Calculation of the Masses of All Fundamental Elementary Particles with an Accuracy of Approx. 1%" [Journal of Modern Physics, 2010, 1, 300-302]
Mass spectrum of localized states (elementary particles) of single quantum system is studied in the framework of Heisenberg's scheme. Localized states are understood as cyclic representations of a group of fundamental symmetry (Lorentz group) within a Gelfand-Neumark-Segal construction. It is shown that state masses of lepton (except the neutrino) and hadron sectors of matter spectrum are proportional to the rest mass of electron with an accuracy of $0,41\%$.
The relations between the hidden symmetries of the six-dimensional pseudo-Euclidean space with signature (+++ -- ) and the conserved quantum characteristics of elementary particles is established. The hidden symmetries are brought out by the various forms of representation of the pseudo-Euclidean space metric with the aid of spinors and hyperbolic complex numbers. Using the emerging hidden symmetry groups one can disclose such conserved quantum characteristics as spin, isospin, electric and baryon charges, hypercharge, color and flavor. One can also predict the exact number of such conserved q…
We show how chirality emerges naturally from an embedding of the standard model of particle physics into $E_{8(-24)}$. The well-known argument that there is no chiral theory of fundamental physics in $E_8$ is avoided by implementing chirality not as a property of the complexified Lorentz group, but as a property of the complex representations of the real Lorentz group, combined with a real scalar. This avoids the problems of complexification, and ensures that the model is completely contained in the real Lie group.
The high-temperature limit of Standard Model generated by the contractions of gauge groups is discussed. Contraction parameters of gauge group $SU(2)$ of Electroweak Model and gauge group $SU(3)$ of Quantum Chromodynamics are taken identical and tending to zero when temperature increase. Properties of the elementary particles change drastically at the infinite temperature limit: all particles lose masses, all quarks are monochromatic. Electroweak interactions become long-range and are mediated by the neutral currents. Particles of different kind do not interact. It looks like some stratificati…
Elementary Cycles Theory is a self-consistent, unified formulation of quantum and relativistic physics. Here we introduce its basic quantum aspects. On one hand, Newton's law of inertia states that every isolated particle has persistent motion, i.e. constant energy and momentum. On the other hand, the wave-particle duality associates a space-time recurrence to the elementary particle energy-momentum. Paraphrasing these two fundamental principles, Elementary Cycles Theory postulates that every isolated elementary constituent of nature (every elementary particle) must be characterized by persist…
A novel theory of the structure of elementary particles is outlined. The proposed relativistic covariant space-time approach supposes that all massive particles are composite particles formed by massless elementary particles with opposite four-dimensional (4D) helicity. The attraction between two basic particles originates from their mutual 4D density, which depends only on their 4D distance. The approach enables a consistent description of the internal structure of massive elementary particles including the origin of their spin, their mass, and the sign of their charge. The 4D rotational Hami…
Schr{ö}dinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the Dirac equation in an arbitrary electromagnetic or Yang--Mills field. This suggests some "symmetry" between positive and negative frequencies and, therefore, particles and antiparticles, so the author previously considered a description of one-particle wave functions as plasma-like collections of a large number of particles and antiparticles. The description has some similarities with Bohmian mech…
Top-Quark Mass Data and the Sum of Quasi-Degenerate Neutrino Masses (One small electroweak-bound e-parameter organizes elementary particle 3-flavor phenomenology)
Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituents of the hadrons, a) have an approximate flavor SU(3) symmetry, b) have an exact color SU(3) symmetry, and c) as spin 1/2 particles, have a Lorentz SO(3,1) symmetry. So does a 3D harmonic oscillator. a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 fundamental modes of oscillation are not identical. b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three co…
