A Time Operator and the Time-Of-Arrival Problem in Quantum Field Theory

The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we construct one-particle states of massive Klein-Gordon theory tha...

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Bibliographic Details
Published in:Foundations of physics Vol. 55; no. 4; p. 56
Main Authors: Colosi, Daniele, Oeckl, Robert
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2025
Springer Nature B.V
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
Hilbert space
History and Philosophical Foundations of Physics
Hyperspaces
Localization
Mathematical functions
Philosophy of Science
Physics
Physics and Astronomy
Probability
Quantum field theory
Quantum Physics
Quantum theory
Relativity Theory
Spacetime
Statistical Physics and Dynamical Systems
Superluminal propagation
ISSN:0015-9018, 1572-9516
Online Access:Get full text
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Summary:The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we construct one-particle states of massive Klein-Gordon theory that are localized on the hypersurface in the temporal as well as two spatial directions. This addresses the longstanding problem of a “time operator" in quantum theory. It is made possible by recent advances in quantization on timelike hypersurfaces and the introduction of evanescent particles. As a first application of time-localized states, we consider the time-of-arrival problem. Our results are in accordance with semiclassical expectations of causal propagation of massless and massive particles. As in the Newton-Wigner case, localization is not perfect, but apparent superluminal propagation is exponentially suppressed.
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ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-025-00866-x