论文标题
迪拉克理论的尺寸减少
Dimensional reduction of the Dirac theory
论文作者
论文摘要
我们通过采用Hadamard的下降方法，从而从三个空间维度降低至两个空间维度。我们首先考虑自由案例，其中运动是由狄拉克方程确定的，然后由Dirac-Maxwell方程控制的动态电磁场的耦合。我们发现，沿一个空间方向的不变性将两种脱钩的理论分开。另一方面，在存在电磁场的情况下，在2+1个维度中提供了更复杂的理论，其中通过使用协变量衍生物来扩展下降方法。方程式简化，但是仅当考虑特定类别的解决方案类别时，不同的物理部门之间的脱钩才会发生。
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical electromagnetic field, governed by the Dirac-Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an electromagnetic field provides a more complicated theory in 2+1 dimensions, in which the method of descent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.
