Related papers: Lanczos - Einstein - Petiau: From Dirac's equation…
When Einstein formulated his special relativity in 1905, he established the law of Lorentz transformations for point particles. It is now known that particles have internal space-time structures. Particles, such as photons and electrons,…
We represent sixteen-component values "sedeons", generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It…
The space-time symmetry group of a model of a relativistic spin 1/2 elementary particle, which satisfies Dirac's equation when quantized, is analyzed. It is shown that this group, larger than the Poincare group, also contains space-time…
Despite conventional wisdom that spin-1/2 systems have no classical analog, we introduce a set of classical coupled oscillators with solutions that exactly map onto the dynamics of an unmeasured electron spin state in an arbitrary,…
The evolution of light theories began with Isaac Newton's corpuscular model, which explained reflection and refraction but could not account for diffraction and interference. In contrast, Christiaan Huygens proposed a wave theory,…
The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincar\'e group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless…
The Standard Model is an up-to-date theory that best summarizes current knowledge in particle physics. Although some problems still remain open, it represents the leading model which all physicists refer to. One of the pillars which…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The kinematical formalism for describing spinning particles developped by the author is based upon the idea that an elementary particle is a physical system with no excited states. It can be annihilated by the interaction with its…
In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and…
A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and…
The usual action integral of classical electrodynamics is derived starting from Lanczos's electrodynamics -- a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell's equations interpreted…
In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
The second-order equation in the (1/2,0)+(0,1/2) representation of the Lorentz group has been proposed by A. Barut in the 70s. It permits to explain the mass splitting of leptons (e,mu,tau). Recently, the interest has grown to this model…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…
Credible reasons are presented to reveal that many of the lingering century old enigmas, surrounding the behavior of at least an individual quantum particle, can be comprehended in terms of an objectively real specific wave function. This…
I review the paper of Majorana about relativistic particles with arbitrary spin written in 1932. The main motivation for this papers was the dissatisfaction about the negative energy solutions of the Dirac equation. As such, the paper…
The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible states of the particle are just kinematical modifications of any one of them. In this way instead of describing…
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the…