Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910461508714496 |
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| author | De Rosa, Carmine Moretti, Valter |
| author_facet | De Rosa, Carmine Moretti, Valter |
| contents | We introduce and study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of a coherent family of normalized POVMs, one for each said Cauchy surface. We prove that a family of POVMs of this type automatically satisfies a causality condition which generalizes Castrigiano's one and implies it when restricting to flat spacelike Cauchy surfaces. As a consequence no conflict with Hegerfeldt's theorem arises. We furthermore prove that such families of POVMs do exist for massive Klein-Gordon particles, since some of them are extensions of already known spatial localization observables. These are constructed out of positive definite kernels or are defined in terms of the stress-energy tensor operator. Some further features of these structures are investigated, in particular, the relation with the triple of Newton-Wigner selfadjoint operators and a modified form of Heisenberg inequality in the rest $3$-spaces of Minkowski reference frames |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties De Rosa, Carmine Moretti, Valter Mathematical Physics High Energy Physics - Theory Quantum Physics We introduce and study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of a coherent family of normalized POVMs, one for each said Cauchy surface. We prove that a family of POVMs of this type automatically satisfies a causality condition which generalizes Castrigiano's one and implies it when restricting to flat spacelike Cauchy surfaces. As a consequence no conflict with Hegerfeldt's theorem arises. We furthermore prove that such families of POVMs do exist for massive Klein-Gordon particles, since some of them are extensions of already known spatial localization observables. These are constructed out of positive definite kernels or are defined in terms of the stress-energy tensor operator. Some further features of these structures are investigated, in particular, the relation with the triple of Newton-Wigner selfadjoint operators and a modified form of Heisenberg inequality in the rest $3$-spaces of Minkowski reference frames |
| title | Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2402.13894 |