Time of arrival and localization of relativistic particles
arXiv:1807.06533 · doi:10.1063/1.5080930
Abstract
Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to conflict with the requirement of causality. In this paper, we describe particle localization in terms of time-of-arrival observables, defined in terms of the interaction between a quantum field and a measuring apparatus. The resulting probabilities are linear functionals of QFT correlation functions. Specializing to the case of a scalar field, we identify several time-of-arrival observables differing on the way that the apparatus localizes particle-detection records. Maximum localization is obtained for a unique observable that is related to the Newton-Wigner position operator. Finally, we define a measure of localizability for relativistic particles in terms of a novel time-energy uncertainty relation for the variance of the time of arrival.
30 pages.Minor changes, to appear in JMP
References in corpus (5)
- Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival
- Time-of-arrival correlations
- Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
- Time-of-arrival probabilities and quantum measurements: III Decay of unstable states
- Real-time particle-detection probabilities in accelerated macroscopic detectors
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