量子时空定域化：Hegerfeldt粒子分析
Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox
摘要：
在狄拉克约束理论的背景下，分析了相对论性量子力学中的两个相关问题：初始定域粒子的视超光速传播和空间定域对观测者运动的依赖性.通过引入相对论性粒子的时间和能量算符，并将Klein-Gordon方程作为约束条件，得到了一个参数化不变公式。标准的物理希尔伯特空间通过在适当时间上的积分从其中时间和能量是动力学变量的增强希尔伯特空间恢复。它表明，牛顿-维格纳位置算子，在这种描述中是一个常数的运动，作用于增广空间中的状态。具有严格正能量的状态在时间上是非局域的;因此，位置测量在许多时候接收来自代表粒子位置的状态的贡献。表观超光速传播的解释是，由于粒子可能处于假设的初始位置和时间的过去（或未来），它有时间传播到遥远的区域而不超过光速。证明了一个不等式，表明Hegerfeldt悖论完全可以用从一组初始时空点的亚光速传播的假设来解释，这些初始时空点由系统能量的正性所产生的量子时间分布所确定。然而，空间局域化可以通过在不同时间代表粒子的状态之间的量子干涉发生。同一系统对于运动观测者的非定域性是由于空间轴的洛伦兹旋转超出了干涉最小值。
英文摘要：
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's theory of constraints. A parametrization invariant formulation is obtained by introducing time and energy operators for the relativistic particle and then treating the Klein-Gordon equation as a constraint. The standard, physical Hilbert space is recovered, via integration over proper time, from an augmented Hilbert space wherein time and energy are dynamical variables. It is shown that the Newton-Wigner position operator, being in this description a constant of motion, acts on states in the augmented space. States with strictly positive energy are non-local in time; consequently, position measurements receive contributions from states representing the particle's position at many times. Apparent superluminal propagation is explained by noting that, as the particle is potentially in the past (or future) of the assumed initial place and time of localization, it has time to propagate to distant regions without exceeding the speed of light. An inequality is proven showing the Hegerfeldt paradox to be completely accounted for by the hypotheses of subluminal propagation from a set of initial space-time points determined by the quantum time distribution arising from the positivity of the system's energy. Spatial localization can nevertheless occur through quantum interference between states representing the particle at different times. The non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.
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