论文标题
在3D DE STATTER背景上外部电磁场中klein-Gordon方程的精确溶液
Exact solutions of the Klein-Gordon equation in external electromagnetic fields on 3D de Sitter background
论文作者
论文摘要
在这项研究中，我们研究了在3D DE STINTER背景上外部电磁场的情况下，在存在外部电磁场的情况下，在存在外部电磁场的情况下，klein-gordon方程的对称性和可能性的可能性。我们提出了一种用于构建一阶对称代数的算法，并用Lie代数扩展来描述其结构。基于代数$ \ mathfrak {so}（1,3）$的非等价子代数的众所周知的分类，我们在$ \ mathrm {ds} _3 $上获得了电磁场的分类。然后，我们选择了可集成的情况，对于每个情况，我们使用Shapovalov和Shirokov开发的非交通性集成方法构建精确的解决方案。在附录中，我们提出了一种原始代数方法，用于在DE Sitter空间上构建特殊的本地坐标，在该方法中，代数$ \ Mathfrak {so}（SO}（1,3）$的subgebras的基础向量字段具有最简单的形式。
In this study, we investigate the symmetry properties and the possibility of exact integration of the Klein--Gordon equation in the presence of an external electromagnetic field on 3D de Sitter background. We present an algorithm for constructing the first-order symmetry algebra and describe its structure in terms of Lie algebra extensions. Based on the well-known classification of the inequivalent subalgebras of the algebra $\mathfrak{so}(1,3)$, we obtain the classification of the electromagnetic fields on $\mathrm{dS}_3$ admitting first-order symmetry algebras of the Klein-Gordon equation. Then, we select the integrable cases, and for each of them, we construct exact solutions, using the non-commutative integration method developed by Shapovalov and Shirokov. In Appendix, we present an original algebraic method for constructing the special local coordinates on de Sitter space, in which the basis vector fields for subalgebras of the algebra $\mathfrak{so}(1,3)$ have the simplest form.
