Related papers: Infinite Component Relativistic Wave Equations
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
The planar quantum dynamics of spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations are obtained directly from the planar Dirac equation with nonminimum coupling. New…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
The solutions of the arbitrary-spin massless wave equations over ${\bf R}^1 \times H^3$ space are obtained using the generalized coherent states for the Lorentz group. The use of these solutions for the construction of invariant propagators…
One of the highlight of this note is that the author presents the relativistic gravity field that Einstein was looking for. The field is a byproduct of the matter in motion. This field can include both the discrete and continuous…
Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…
In a representation theoretic approach a free q-relativistic wave equation must be such, that the space of solutions is an irreducible representation of the q-Poincare algebra. It is shown how this requirement uniquely determines the q-wave…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
We show that a bound system in momentum space can be treated like a gas of free elementary constituents and a collective excitation of a background field which represents the countless quantum fluctuations generating the binding potential.…
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
Based on the representation theory of the $q$-deformed Lorentz and Poincar\'e symmeties $q$-deformed relativistic wave equation are constructed. The most important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations are…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory…
We consider relativistic charged particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of co-adjoint orbits of the Poincar\'e group. The particle case is meant to clarify some points…
In this paper we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long scale-length limit, where the fields vary on a scale much longer than the localization of the…
We establish exactly solvable models for the motion of neutral particles, electrically charged point and spin particles (U(1) symmetry), isospin particles (SU(2) symmetry), and particles with color charges (SU(3) symmetry) in a…
The exact solution of the Dirac equation and the spectrum of electron quasi-energies in a superposition of the field of a circularly polarized electromagnetic wave and a homogeneous magnetic field parallel to the direction of wave…