论文标题
在均匀空间中狄拉克方程的非共同整合
Noncommutative integration of the Dirac equation in homogeneous spaces
论文作者
论文摘要
我们为均匀空间中的狄拉克方程开发了一种非交通性集成方法。显示具有不变度度的狄拉克方程与均匀空间转换的谎言群体上的方程式相等。这使我们能够有效地应用谎言组线性偏微分方程的非交通性集成方法。这种方法与众所周知的变量分离方法有所不同，并且在某种程度上通常可以补充它。该方法的一般结构用均匀空间的示例说明了，该空间不接受狄拉克方程中变量的分离。但是，狄拉克方程的精确解决方案的基础是通过非交通性集成方法明确构建的。此外，我们使用开发的方法在三维de安慰剂时空$ \ mathrm {ads_ {3}} $中使用开发的方法构建了一组新的精确解决方案。获得的解决方案是根据基本函数的，这是非交通整合方法的特征。
We develop a noncommutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the noncommutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the noncommutative integration method. Also, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time $\mathrm{AdS_{3}}$ using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the noncommutative integration method.
