论文标题
使用自然公理的通勤组件的光子位置运算符构建
Construction of a photon position operator with commuting components from natural axioms
论文作者
论文摘要
获得了具有通勤组件的光子位置算子的一般形式，可获得一些自然公理。该操作员用光子螺旋算子通勤，相对于Bialynicki-Birula标量产品，是Hermitian，并定义为保留横向条件的单一转换。结果表明，使用类似于T. T. Wu和C. N. Yang引入的程序，对于Dirac磁性单极而言，可以通过在$ \ Mathbb {r}^3 \ setMinus \ \ {（0,0,0,0,0,0,0,0）$的$ \ mathbb {r}^3 \ setMinus \} $ \ mathbb {r}^3 \ setMinus \}中的平坦矢量束中的平坦连接来定义光子位置操作员。该观察结果使我们能够在$（\ mathbb {r}^{3} {3} \ setMinus \ {（0,0,0,0）\}）\ times \ times \ times \ mathbb {c}^2 $上重新调整a〜单个光子的量子力学。
A general form of the photon position operator with commuting components fulfilling some natural axioms is obtained. This operator commutes with the photon helicity operator, is Hermitian with respect to the Bialynicki-Birula scalar product and defined up to a unitary transformation preserving the transversality condition. It is shown that, using the procedure analogous to the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac magnetic monopole, the photon position operator can be defined by a flat connection in some trivial vector bundle over $\mathbb{R}^3 \setminus \{(0,0,0)\}$. This observation enables us to reformulate quantum mechanics of a~single photon on $(\mathbb{R}^{3} \setminus \{(0,0,0)\}) \times \mathbb{C}^2$.
