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arXiv · 2407.08841

A time operator and the time-of-arrival problem in quantum field theory

Daniele Colosi·Robert Oeckl
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Abstract

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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Daniele Colosi, Robert Oeckl. 2025-06-30. A time operator and the time-of-arrival problem in quantum field theory. https://doi.org/10.1007/s10701-025-00866-x

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