Abstract

Fundamental properties of the position and spin operators in relativistic quantum mechanics are defined with the Poincaré group. Quantum-mechanical counterparts of the classical position and spin variables are the corresponding operators in the Foldy–Wouthuysen representation but not in the Dirac one. The probabilistic interpretation is valid only for Foldy–Wouthuysen wave functions. The relativistic operators of the position and spin are discussed.

中文翻译：

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庞加莱群以及位置和自旋算子

摘要

相对论量子力学中位置和自旋算子的基本性质是用庞加莱群定义的。经典位置和自旋变量的量子力学对应物是 Foldy-Wouthuysen 表示中的相应算子，但在狄拉克表示中则不是。概率解释仅对 Foldy-Wouthuysen 波函数有效。讨论了位置和自旋的相对论算子。