复数形式的Majorana-Oppenheimer型麦克斯韦方程组，Riemann S_{3}和Lobachevsky H_{3}空间中具有对称性的解
Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces
摘要：
本文将麦克斯韦电动力学中的Riemann-Silberstein- Majorana - Oppenheimer复形式推广到任意伪黎曼时空的情形。该方法在静态宇宙学爱因斯坦模型的背景下精确求解麦克斯韦方程组，用特殊的柱坐标参数化，实现为常正曲率的黎曼空间。得到了依赖于空间曲率半径和三个参数的电磁模式的离散频谱，并构造了相应的基本电磁解。在椭圆模型的情况下，一部分构造的解决方案应被拒绝的连续性考虑。对双曲罗巴切夫斯基模型下的麦克斯韦方程组也作了类似的处理，构造了相应柱坐标下电磁解的完备基，没有出现电磁模频率的量子化。
英文摘要：
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.
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