5 research outputs found
Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in
Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian
space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock -
Ivanenko. In this approach, the Maxwell equations are solved exactly on the
background of static cosmological Einstein model, parameterized by special
cylindrical coordinates and realized as a Riemann space of constant positive
curvature. A discrete frequency spectrum for electromagnetic modes depending on
the curvature radius of space and three parameters is found, and corresponding
basis electromagnetic solutions have been constructed explicitly. In the case
of elliptical model a part of the constructed solutions should be rejected by
continuity considerations. Similar treatment is given for Maxwell equations in
hyperbolic Lobachevsky model, the complete basis of electromagnetic solutions
in corresponding cylindrical coordinates has been constructed as well, no
quantization of frequencies of electromagnetic modes arises.Comment: 39 page
Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell
electrodynamics in vacuum is investigated within the matrix formalism. The
matrix form of electrodynamics includes three real 4 \times 4 matrices. Within
the squaring procedure we construct four formal solutions of the Maxwell
equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem
of separating physical electromagnetic waves in the linear space
\lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3}
is investigated, several particular cases, plane waves and cylindrical waves,
are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk,
Belaru
On exact solutions for quantum particles with spin S= 0, 1/2, 1 and de Sitter event horizon
Exact wave solutions for particles with spin 0, 1/2 and 1 in the static
coordinates of the de Sitter space-time model are examined in detail. Firstly,
for a scalar particle, two pairs of linearly independent solutions are
specified explicitly: running and standing waves. A known algorithm for
calculation of the reflection coefficient on the background of
the de Sitter space-time model is analyzed. It is shown that the determination
of R_{\epsilon j} requires an additional constrain on quantum numbers \epsilon
\rho / \hbar c >> j, where \rho is a curvature radius. When taken into account
of this condition, the R_{\epsilon j} vanishes identically. It is claimed that
the calculation of the reflection coefficient R_{\epsilon j} is not required at
all because there is no barrier in an effective potential curve on the
background of the de Sitter space-time. The same conclusion holds for arbitrary
particles with higher spins, it is demonstrated explicitly with the help of
exact solutions for electromagnetic and Dirac fields.Comment: 30 pages. This paper is an updated and more comprehensive version of
the old paper V.M. Red'kov. On Particle penetrating through de Sitter
horizon. Minsk (1991) 22 pages Deposited in VINITI 30.09.91, 3842 - B9