A time operator and the time-of-arrival problem in quantum field theory
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912461350764544 |
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| author | Colosi, Daniele Oeckl, Robert |
| author_facet | Colosi, Daniele Oeckl, Robert |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A time operator and the time-of-arrival problem in quantum field theory Colosi, Daniele Oeckl, Robert High Energy Physics - Theory Quantum Physics 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. |
| title | A time operator and the time-of-arrival problem in quantum field theory |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2407.08841 |