事件在时空中的局部化
Localization of Events in Space-Time
摘要：
本文讨论时空中事件的量子坐标，它被量子物体个体化。已知这些观测量不能用自伴算子或相应的谱投影值测度来描述。我们通过闵可夫斯基时空中的一个正算子值测度来描述它们，该测度满足关于庞加莱群的一个适当的协方差条件。这个随机测度决定了事件坐标的测量给出属于时空中给定集合的结果的概率。我们证明了这个测度在真空和单粒子态上必须为零，而这不能定义任何事件。给出了Poincare协变测度的一般表达式。我们定义了重心事件，它位于质心的世界线上，我们找到了一个简单的表达式，其坐标的平均值。最后，我们讨论了允许确定任意精度的坐标的条件。
英文摘要：
The present paper deals with the quantum coordinates of an event in space-time, individuated by a quantum object. It is known that these observables cannot be described by self-adjoint operators or by the corresponding spectral projection-valued measure. We describe them by means of a positive-operator-valued (POV) measure in the Minkowski space-time, satisfying a suitable covariance condition with respect to the Poincare' group. This POV measure determines the probability that a measurement of the coordinates of the event gives results belonging to a given set in space-time. We show that this measure must vanish on the vacuum and the one-particle states, which cannot define any event. We give a general expression for the Poincare' covariant POV measures. We define the baricentric events, which lie on the world-line of the centre-of-mass, and we find a simple expression for the average values of their coordinates. Finally, we discuss the conditions which permit the determination of the coordinates with an arbitrary accuracy.
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