2024/02/21 by Carmine De Rosa, Valter Moretti · 1 voice
Mathematics · Physics and Astronomy · #Cauchy distribution #Causal structure #Classical mechanics #Geometric Analysis and Curvature Flows #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Observable #Particle (ecology) #Physics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Spacetime #Theoretical physics #advanced mathematical theories #hep-th #math-ph #quant-ph
paper · pdf · doi:10.1007/s11005-024-01817-9
arxiv published 2024/02/21 · arxiv updated 2024/05/03 · openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.