Related papers: Complex representation theory of the electromagnet…
A self-contained derivation of the formalism describing Weyl, Majorana and Dirac fields from a unified perspective is given based on a concise description of the representation theory of the proper orthochronous Lorentz group. Lagrangian…
A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an objective extra space dimension. "Particle"…
Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self…
I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We present new aspects of the electromagnetic field by introducting the natural potentials. These natural potentials are suitable for constructing the first order distortions of the metric tensor of Complex Relativity - the theory combining…
We consider the representations of the optical Dirac equation, especially ones where the Hamiltonian is purely real-valued. This is equivalent, for Maxwell's equations, to the Majorana representation of the massless Dirac (Weyl) equation.…
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the…
It is recently discovered that the usual transformations of the three-dimensional (3D) vectors of the electric and magnetic fields differ from the Lorentz transformations (LT) (boosts) of the corresponding 4D quantities that represent the…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
In the paper a new class of exact localized solutions of Dirac's equation in the field of a circularly polarized electromagnetic wave and a constant magnetic field is presented. These solutions possess unusual properties and are applicable…
The present paper is the continuation of the paper "Nonlinear field theory I". In the paper it is shown that a fully correspondence between the quantum and the nonlinear electromagnetic forms of the Dirac electron theory exists, so that…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
It is shown that the hypercomplex Dirac equation describes the system of connected fields: 4-scalar, 4-pseudoscalar, 4-vector, 4-pseudo-vector and antisymmetric 4-tensor second rank field. If mass is assumed to be zero this system splits…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
A compact and elegant description of the electromagnetic fields in media and in vacuum is attained in the differential forms formalism. This description is explicitly invariant under diffeomorphisms of the spacetime so it is suitable for…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…