电子的量子六球面观测量
Quantum Hexaspherical Observables for Electrons
摘要：
建立在共形动力学对称（SO（4，2））上的相对论电子的一种新的量子代数描述最近被提出来处理时空中的局域化。本文证明了电子的局域化可以用SO（4，2）矢量的分量来表示，SO（4，2）矢量是经典射影几何六球面坐标的量子推广。这个向量在变换到均匀加速坐标系下的位移由SO（4，2）旋转描述。六球面观测量也允许人们在一种与相同的动力学对称性明确相容的形式下表示自由降落的量子定律。
英文摘要：
A new quantum algebraic description of relativistic electrons, built on a conformal dynamical symmetry (SO(4,2)), has recently been proposed to treat localization in space-time. It is shown here that localization of an electron may be represented by components of a SO(4,2) vector which are quantum generalizations of the hexaspherical coordinates of classical projective geometry. The shift of this vector under transformations to uniformly accelerated frames is described by SO(4,2) rotations. Hexaspherical observables also allow one to represent the quantum law of free fall under a form explicitly compatible with the same dynamical symmetry.
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