论文标题
任意空间维度中狄拉克方程的维度降低
Dimensional reduction of the Dirac equation in arbitrary spatial dimensions
论文作者
论文摘要
我们研究了以任意数量的空间维度在Minkowski时空中提出的DIRAC理论的维数降低的一般特性。这是通过应用Hadamard的下降方法来完成的，该方法包括将低维理论构想为沿额外空间坐标均匀的高维理论的专业化。我们表明，狄拉克方程将减小到一个dirac方程或两个脱钩的狄拉克方程，具体取决于较高的歧管分别具有均匀或奇数的空间维度。此外，我们构建并讨论了表示该过程变得明显并很容易迭代的表示形式的明确层次结构。
We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which consists in conceiving low-dimensional theories as a specialization of high-dimensional ones that are uniform along the additional space coordinate. We show that the Dirac equation reduces to either a single Dirac equation or two decoupled Dirac equations, depending on whether the higher-dimensional manifold has even or odd spatial dimensions, respectively. Furthermore, we construct and discuss an explicit hierarchy of representations in which this procedure becomes manifest and can easily be iterated.
