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.

Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties / De Rosa, Carmine; Moretti, Valter. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 2024, 114:(2024), pp. 7201-7260. [10.1007/s11005-024-01817-9]

Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties

De Rosa, Carmine;Moretti, Valter
2024-01-01

Abstract

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.
2024
De Rosa, Carmine; Moretti, Valter
Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties / De Rosa, Carmine; Moretti, Valter. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 2024, 114:(2024), pp. 7201-7260. [10.1007/s11005-024-01817-9]
File in questo prodotto:
File Dimensione Formato  
ContoDUE-2.pdf

embargo fino al 28/05/2025

Descrizione: Preprint definitivo
Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 607.57 kB
Formato Adobe PDF
607.57 kB Adobe PDF   Visualizza/Apri
s11005-024-01817-9.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 856.29 kB
Formato Adobe PDF
856.29 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/408651
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact