Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time

The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $\alpha^{b}$. In presence of media matrix form requires two sets of $4 \times 4$ matrices, $\alpha^{b}$ and $\beta^{b}$ -- simple and symmetrical realization of which is given. Relation of $\alpha^{b}$ and $\beta^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form, based on the use of two electromagnetic 4-vector, is studied and discussed. Extension of the 3-vector complex matrix formalism to arbitrary Riemannian space-time in accordance with tetrad method by Tetrode-Weyl-Fock-Ivanenko is performed.Comment: 32pages. Proccedings of the 14th Conference-School "Foundation & Advances in Nonlinear Science", Minsk, September 22-25, 2008. P. 20-49; ed. V.I. Kuvshinov, G.G. Krylov, Minsk, 200

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

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

ХАРАКТЕРИСТИКИ ОТРАЖЕНИЯ И ПЕРЕДАЧИ ЭЛЕКТРОМАГНИТНОГО ИЗЛУЧЕНИЯ ДВУХСЛОЙНЫХ СТРУКТУР НА ОСНОВЕ ОКСИДОВ ПЕРЕХОДНЫХ МЕТАЛЛОВ

The aim of the work, the results of which are presented in the framework of the article, was to study the of electromagnetic radiation interaction laws in the frequency range 0.7…17 GHz with two-layer structures, the surface layer of which was made using powdered titanium dioxide, and the inner layer was made using a powder material based on oxide ferric iron. The thickness of the layers of the studied structures varied from 0.3 to 1 cm. To achieve this goal, theobjectives associated with the development of a methodology for the manufacture of multilayer structures based on composite materials containing transition metal oxides, as well as with the measurement of such structures samples electromagnetic radiation reflection and transmission coefficients in the frequency range 0.7...17 GHz. These measurements were carried out using a panoramic meter of reflection and transmission coefficients SNA 0.01–17. Based on the obtained measurement results, it was shown that in the frequency range 0.7…2 GHz, the lowest values of electromagnetic radiation reflection coefficient, reaching –20 dB, are characterized by structures whose surface layer thickness is 1 cm, and in the range 2 ... 17 GHz – structures, thickness the surface layer of which is 0.5 or 1 cm (depending on the thickness of the inner layer). The values of electromagnetic radiation transmission coefficient in the frequency range of 0.7...17 GHz of such structures reach –23 dB. Based on the results of the study, it is proposed to use the considered structures in the process of creating shielded rooms or improving the latter (for example, in cases, when it's necessary to reduce the level of passive interference in rooms shielded with metal materials).Цель работы, результаты которой представлены в рамках статьи, заключалась в исследовании закономерностей взаимодействия электромагнитного излучения диапазона частот 0,7…17 ГГц с двухслойными структурами, поверхностный слой которых изготовлен с использованием порошкообразного диоксида титана, а внутренний слой – с использованием порошкообразного материала на основе оксида трехвалентного железа. Толщина слоев исследованных структур изменялась в пределах от 0,3 до 1 см. Для достижения поставленной цели были решены задачи, связанные с разработкой методики изготовления многослойных структур на основе композиционных материалов, содержащих оксиды переходных металлов, а также с измерением значений коэффициентов отражения и передачи электромагнитного излучения в диапазоне частот 0,7…17 ГГц образцов таких структур. Указанные измерения проводились с использованием панорамного измерителя коэффициентов отражения и передачи SNA 0.01–17. На основе полученных результатов измерений показано, что в диапазоне частот 0,7…2 ГГц наименьшими значениями коэффициента отражения электромагнитного излучения, достигающими –20 дБ, характеризуются структуры, толщина поверхностного слоя которых составляет 1 см, а в диапазоне 2…17 ГГц – структуры, толщина поверхностного слоя которых составляет 0,5 или 1 см (в зависимости от толщины внутреннего слоя). Значения коэффициента передачи электромагнитного излучения в диапазоне частот 0,7…17 ГГц таких структур достигают величины –23 дБ. С учетом полученных результатов исследования предложено использовать рассмотренные структуры в процессе создания экранированных помещений или усовершенствования последних (например, в случаях, когда необходимо снизить уровень пассивных помех в помещениях, экранированных с помощью металлических материалов)

РАДИОЭКРАНИРУЮЩИЕ СВОЙСТВА КОМПОЗИТОВ НА ОСНОВЕ ДИОКСИДА ТИТАНА

The study of regularities of interaction of electromagnetic radiation of the radiofrequency range (0.7…17 GHz) with composites based on titanium dioxide, depending on the type of binder of the latter was realized. The consist of the investigated composites, which is optimal for reduction of the energy of electromagnetic waves reflected from metallic materials was determined on the basis of obtained results.Выполнено исследование закономерностей взаимодействия электромагнитного излучения радиочастотного диапазона (0,7…17 ГГц) с композитами на основе диоксида титана в зависимости от типа связующего последних. На основе полученных результатов для исследованных композитов определен оптимальный состав, при котором они могут быть использованы в целях уменьшения энергии электромагнитных волн, отражаемых от металлических материалов

Effect of a powerful low-frequency signal on an anisotropic medium over hydrocarbon

The article analyses the interaction of a powerful low-frequency signal with an anisotropic medium over hydrocarbon deposits. The behaviour of the real and phase components of the surface impedance of the medium above the deposit in the mode of dual-frequency signals is studied. The analysis of the components of the surface impedance of the medium over hydrocarbons for electromagnetic waves with right and left circular polarizations is carried out depending on the permittivity and frequency of the probing signals. The obtained research results can be used in exploration geophysics to identify the environment above the deposits by the size and nature of the material and phase components of the surface impedance of the surface layer above the hydrocarbons