Related papers: Generalized Relativistic Wave Equations with Intri…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
Magnetic effects on free electron systems have been studied extensively in the context of spin-to-orbital angular momentum conversion. Starting from the Dirac equation, we derive a fully relativistic expression for the energy of free…
The ``Jackiw-Nair'' non-relativistic limit of the relativistic anyon equations provides us with infinite-component wave equations of the Dirac-Majorana-Levy-Leblond type for the ``exotic'' particle, associated with the two-fold central…
We consider for the first time the solutions of Klein-Gordon equation in gravitational field of {\em a massive} point source in GR. We examine numerically the basic bounded quantum state and the next few states in the discrete spectrum for…
We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $ f(x,t) - i \mu \gamma^0 \Psi$, where both $f$ and $\Psi$ are…
In this paper, we introduce an extension of the Dirac equation, very similar to Dirac oscillator, that gives stationary localized wave packets as eigenstates of the equation. The extension to the Dirac equation is achieved through the…
In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr\"odinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which…
Recently, two different proofs for large and intermediate-size solitary waves of the nonlocally dispersive Whitham equation have been presented, using either global bifurcation theory or the limit of waves of large period. We give here a…
In this paper, we consider the problem of nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation with Dirichlet boundary conditions. The wave dynamics are subject to a dissipative nonlinear velocity…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
We show that, contrary to the statements made by many authors, the backflow is not a nonclassical effect. The backflow is a characteristic feature of solutions of the wave equations: quantum and classical. We present simple solutions of the…
We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…
The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should…
It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves…
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…
We consider wave functions in the Hilbert space $\mathcal{H}=L^2(\mathbb{R}^3,\mathbb{C}^4)$ of a single Dirac particle, specifically from the positive-energy subspace $\mathcal{H}_+$ of the free Dirac Hamiltonian. Over the decades, various…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of point particles in special relativity…
Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy,…