Related papers: A Simple Five-Dimensional Wave Equation for a Dira…
The Fermi acceleration mechanism is a significant source of cosmic rays. When the width of a potential well changes over time, the velocity of particles within the well also changes. For quantum systems, such dynamics should be described by…
We carry out a constructive review of non-standard solutions of relativistic wave equations. Such solutions are obtained via splitting of relativistic wave equations written in spinor form. All these solutions are also solutions of the…
First we argue in an informal, qualitative way that it is natural to enlarge space-time to five dimensions to be able to solve the problem of elementary particle masses. Several criteria are developed for the success of this program.…
Two-component spinors are the basic ingredients for describing fermions in quantum field theory in four space-time dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman…
It is argued from geometrical, group-theoretical and physical points of view that in the framework of QCD it is not only necessary but also possible to modify the Dirac equation so that correspondence principle holds valid. The Dirac wave…
In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a…
We construct wave functions and Dirac operator of spin $1/2$ fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly $SO(5)_q$ covariant. We evaluate the engenvalue of…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
We consider a electron in a external field in D=5, through the Dirac equation in the Galilean symmetry approach, and in the Lorentz symmetry approach; from these we perform the nonrelativistic limit, then we procede the supersymmetry of the…
The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave…
The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular…
The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…
A relativistic equation is proposed for the bound state of two particles, which is in accord with the boundary condition for the propagation of the negative-energy states and reduces to the (one-body)Dirac equation in the infinite limit of…
The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated.…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…
We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved…
The quantum theory of relativistic particles, based on the first quantization technique similar to that used by Schroedinger and Dirac in formulating quantum mechanics, is reconsidered on the basis of a photon-like dispersion relation…