Related papers: Dirac, Schroedinger, and Maxwell equations in scal…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
A de Broglie-Bohm like model of Dirac equation, that leads to the correct Pauli equations for electrons and positrons in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum…
Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…
It is shown that a Dirac(-type) equation for a rank-two bi-spinor field on Minkowski (configuration) spacetime furnishes a Lorentz-covariant quantum-mechanical wave equation in position-space representation for a single free photon. This…
Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for…
This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory.…
Using post-Galilean space and time derivatives transformations and quantum mechanics, we have found a new particle-wave equation besides the Klein-Gordon equation describing a spinless scalar particle. This new equation can also be obtained…
Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies…
It is shown that the concept of elementary resonator in the theory of thermal radiation implies the indivisible connection between particles (photons) and electromagnetic waves. This wave-particle duality covers both the Wien and…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior.…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
Fundamental solutions for the free Dirac electron and Einstein photon equations in position coordinates are constructed as matrix valued functionals on the space of bump functions. It is shown that these fundamental solutions are related by…
Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically "periodic phenomena". However, after nearly 90 years, the physical origin of such undulatory mechanics remains…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…