论文标题
在1+1和2+1维度中适当的相对论位置操作员
Proper relativistic position operators in 1+1 and 2+1 dimensions
论文作者
论文摘要
我们通过在其天然维度中使用平等延伸的庞加莱群体的协变代表来重新审视1+1和2+1维度的狄拉克理论。奇偶校验运算符在得出这两种理论中的波动方程中都起着至关重要的作用。我们研究了两个位置运算符，一个规范的一个和一个协变量，该算体成为粒子位置算子投射到粒子子空间上的粒子位置。在1+1个尺寸中，粒子位置操作员而不是规范位置操作员提供了保守的Lorentz发电机。规范位置运算符定义的质量矩需要额外的非物理自旋样算子，以在1+1个维度中成为保守的Lorentz发电机。在2+1个维度中，规范位置算子给出的轨道角动量和旋转角动量的总和成为运动的常数。但是，轨道和旋转角动量不会单独保存。另一方面，粒子位置算子给出的轨道角动量及其相应的自旋角动量分别成为运动常数。
We have revisited the Dirac theory in 1+1 and 2+1 dimensions by using the covariant representation of the parity-extended Poincaré group in their native dimensions. The parity operator plays a crucial role in deriving wave equations in both theories. We studied two position operators, a canonical one and a covariant one that becomes the particle position operator projected onto the particle subspace. In 1+1 dimensions the particle position operator, not the canonical position operator, provides the conserved Lorentz generator. The mass moment defined by the canonical position operator needs an additional unphysical spin-like operator to become the conserved Lorentz generator in 1+1 dimensions. In 2+1 dimensions, the sum of the orbital angular momentum given by the canonical position operator and the spin angular momentum becomes a constant of motion. However, orbital and spin angular momentum do not conserve separately. On the other hand the orbital angular momentum given by the particle position operator and its corresponding spin angular momentum become a constant of motion separately.
