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

• URL: http://arxiv.org/abs/2402.13894v4
• Date: Fri, 3 May 2024 14:37:26 GMT
• Title: Quantum particle localization observables on Cauchy surfaces of Minkowski spacetime and their causal properties
• Authors: Carmine De Rosa, Valter Moretti,
• Abstract summary: We study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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

Related papers

• A relativistic statistical field theory on a discretized Minkowski lattice with quantum-like observables [0.0]
  A relativistic statistical field theory is constructed for a fluctuating complex-valued scalar field on a discretized Minkowski lattice. A Hilbert space of observables is then constructed from functionals of the fluctuating complex-valued scalar field with an inner product defined in terms of expectation values of the functionals. A bosonic Fock space is then constructed from the Hilbert space and creation and operators that act on the Fock space are defined.
  arXiv  Detail & Related papers  (2024-05-30T16:41:25Z)
• On the Relativistic Spatial Localization for massive real scalar Klein-Gordon quantum particles [0.0]
  I rigorously analyze a proposal, introduced by D.R.Terno, about a spatial localization observable for a Klein-Gordon massive real particle. I prove that these POVMs are actually a kinematic deformation of the Newton-Wigner PVMs. The validity of the complete Castrigiano's causality requirement is also proved for a notion of spatial localization which generalizes Terno's one in a natural way.
  arXiv  Detail & Related papers  (2023-04-04T21:34:57Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• From locality to irregularity: Introducing local quenches in massive scalar field theory [68.8204255655161]
  We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension. We identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables.
  arXiv  Detail & Related papers  (2022-05-24T18:00:07Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Dynamical C*-algebras and kinetic perturbations [0.0]
  The framework of dynamical C*-algebras for scalar fields in Minkowski space is extended to theories with locally kinetic terms. Concrete representations of the abstract scattering operators, inducing this motion, are known to exist on Fock space.
  arXiv  Detail & Related papers  (2020-08-05T10:19:55Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Entanglement of Local Operators and the Butterfly Effect [0.0]
  We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture.
  arXiv  Detail & Related papers  (2020-05-28T19:04:47Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory [0.0]
  Explicit construction of local observable algebras in quasi-Hermitian quantum theories is derived in both the tensor product model of locality and in models of free fermions. Despite the locality of the Hamiltonian, local observables do not exist in generic collections of sites in the lattice.
  arXiv  Detail & Related papers  (2020-02-11T21:46:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.