The Dirac Equation and the Superluminal Electron Model

A historical revew of the development of the dirac equation is given emphasising the connections with the principles of quontom mechanics. We argue that a consistent relativistic quantisation demands the building of a multiparticle theory from the outset that is a theory where the particle number is not a constant but can change over time and that because quontom field theory obey's this requirement it has been found to be able to quontise systems subject to the constraints of special relativity.

New Dirac Equation from the View Point of Particle, 2012

Solution of the Dirac equation with pseudospin symmetry for a new harmonic oscillatory ring-shaped noncentral potential J. Math. Phys. 53, 082104 (2012) Effect of tensor interaction in the Dirac-attractive radial problem under pseudospin symmetry limit J. Math. Phys. 53, 082101 (2012) Asymptotic stability of small gap solitons in nonlinear Dirac equations J. Math. Phys. 53, 073705 (2012) On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization J. Math. Phys. 53, 063503 (2012) Quasi-exact treatment of the relativistic generalized isotonic oscillator Abstract. According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the "field". In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we rewrite and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.

arXiv: General Physics, 2020

We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffman's work on discrete physics, iterants and Majorana Fermions and the work on nilpotent structures and the Dirac equation of Peter Rowlands. We give an expression in split quaternions for the Majorana Dirac equation in one dimension of time and three dimensions of space. Majorana discovered a version of the Dirac equation that can be expressed entirely over the real numbers. This led him to speculate that the solutions to his version of the Dirac equation would correspond to particles that are their own anti-particles. It is the purpose of this paper to examine the structure of this Majorana-Dirac Equation, and to find basic solutions to it by using the nilpotent technique. We succeed in this aim and describe our results.

Annals of Physics, 1988

We discuss in detail two supersymmetries of the 4-dimensional Dirac operator D-italic-dash-bar² where D-italic-dash-bar = partial-dash-bar-ieA-italic-dash-bar, namely the usual chiral supersymmetry and a separate complex supersymmetry. Using SUSY methods developed to categorize solvable potentials in 1-dimensional quantum mechanics we systematically study the cases where the spectrum, eigenfunctions, and S-matrix of D-italic-dash-bar² can be obtained analytically. We relate these solutions to

1995

We show that Maxwell equations and Dirac equation (with zero mass term) have both subluminal and superluminal solutions in vacuum. We also discuss the possible fundamental physical consequences of our results.

Dynamical geometrical models of the electron and the photon are proposed which are composed of sheets of electric charge moving at superluminal velocities in closed and open helical paths respectively. In both models, the sheets of electric charge always internally travel faster than the speed of light, and the size, structure, wavelengths and helical motions of these sheets of electric charge correspond to their energy, momentum and angular momentum, and the electron's magnetic moment to first order. The photon and electron models are closely related through the geometry and dynamics of electron/positron pair production from a photon, resulting in the quantum mechanical 720-degrees rotational symmetry of the electron model. When the electron model moves as a whole with velocity v, it is found that its internal structure generates the electron's de Broglie wavelength L = h / mv , due to internal photon-like Doppler wavelength shifts and wave interference. The electron model also increases its total energy (and therefore its mass) with its velocity in accordance with special relativity, due to the increased net energy associated with the Doppler-shifted frequency of the circulating charged photon-like entity that composes the electron model. Due to the constancy of the electron's angular momentum with velocity, a relativistically moving electron model is found to decrease in size with velocity so as to be consistent with experimental determinations of the maximum size of an electron from high energy scattering experiments. The two models illustrate a new concept of quantum wave-particle duality, where the form of the charged sheets (two in the photon and one in the electron) constitute the particle and their superluminal motion constitutes the wave. This modeling approach predicts that there are two varieties of right circularly polarized photon (and also two types of left circularly polarized photon), depending on whether the positive or negative charge sheet is in front in the photon's direction of motion, and two varieties of negative electron (and two varieties of positron), depending on whether the electric charge sheet in the electron moves forward clockwise or counterclockwise in its closed helical structure. These 2 predicted varieties of the present photon and electron should be distinguishable by the different magnetic fields that they would produce.

Physical Review A, 1990

The quantum theory of a magnetic electron lens with rotational symmetry about its straight optic axis has recently been studied entirely on the basis of the Dirac equation [R.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dyna...

Physica Scripta, 2012

This paper reexamines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.