Relational Observables in Group Field Theory

• URL: http://arxiv.org/abs/2412.14622v1
• Date: Thu, 19 Dec 2024 08:19:38 GMT
• Title: Relational Observables in Group Field Theory
• Authors: Luca Marchetti, Edward Wilson-Ewing,
• Abstract summary: We construct relational observables in group field theory (GFT) in terms of covariant positive operator-valued measures (POVMs) We focus on matter quantum reference frames; this can be generalized to other types of frames within the same POVM-based framework. We find that our quantum reference frame-based relational observables overcome the intrinsic limitations of previous proposals while reproducing the same limit results concerning expectation values of the number and volume operators on coherent states.
• Score: 0.0
• License:
• Abstract: We construct relational observables in group field theory (GFT) in terms of covariant positive operator-valued measures (POVMs), using techniques developed in the context of quantum reference frames. We focus on matter quantum reference frames; this can be generalized to other types of frames within the same POVM-based framework. The resulting family of relational observables provides a covariant framework to extract localized observables from GFT, which is typically defined in a perspective-neutral way. Then, we compare this formalism with previous proposals for relational observables in GFT. We find that our quantum reference frame-based relational observables overcome the intrinsic limitations of previous proposals while reproducing the same continuum limit results concerning expectation values of the number and volume operators on coherent states. Nonetheless, there can be important differences for more complex operators, as well as for other types of GFT states. Finally, we also use a specific class of POVMs to show how to project states and operators from the more general perspective-neutral GFT Fock space to a perspective-dependent one where a scalar matter field plays the role of a relational clock.

Related papers

• Revisiting Self-Supervised Heterogeneous Graph Learning from Spectral Clustering Perspective [52.662463893268225]
  Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. Existing SHGL methods encounter two significant limitations. We introduce a novel framework enhanced by rank and dual consistency constraints.
  arXiv  Detail & Related papers  (2024-12-01T09:33:20Z)
• Operational Quantum Frames: An operational approach to quantum reference frames [0.0]
  We introduce an operational notion of a quantum reference frame -- which is defined as a quantum system equipped with a covariant positive operator-valued measure (POVM) We show that when the frame is localizable, meaning that it allows for states that give rise to a highly localized probability distribution of the frame's observable, by restricting the relative description upon such localized frame preparation we recover the usual, non-relational formalism of quantum mechanics.
  arXiv  Detail & Related papers  (2023-04-14T09:30:35Z)
• Operational Quantum Reference Frame Transformations [0.0]
  We provide a general, operationally motivated framework for quantum reference frames and their transformations. The work is built around the notion of operational equivalence, in which quantum states that cannot be physically distinguished are identified. We give an explicit realisation in the setting that the initial frame admits a highly localized state with respect to the frame observable.
  arXiv  Detail & Related papers  (2023-03-24T13:58:21Z)
• Quantum Reference Frames on Finite Homogeneous Spaces [0.0]
  We focus on the case that the reference observable is the canonical covariant projection valued measure on the given space. We show that this gives rise to a rank-one covariant POVM on the group, which can be seen as a system of coherent states.
  arXiv  Detail & Related papers  (2023-02-10T16:16:18Z)
• Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systems [97.12538243736705]
  We study Reinforcement Learning for partially observable dynamical systems using function approximation. We propose a new textitPartially Observable Bilinear Actor-Critic framework, that is general enough to include models such as POMDPs, observable Linear-Quadratic-Gaussian (LQG), Predictive State Representations (PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPs and observable POMDPs with latent low-rank transition.
  arXiv  Detail & Related papers  (2022-06-24T00:27:42Z)
• Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance [0.0]
  We describe a completely general and non-perturbative framework for constructing dynamical reference frames. Our formalism refutes the commonly claimed non-existence of local gravitational bulk physics.
  arXiv  Detail & Related papers  (2022-06-02T17:52:40Z)
• Self-adjoint extension schemes and modern applications to quantum Hamiltonians [55.2480439325792]
  monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator theory and in applications to quantum mechanics. A number of models are discussed, which are receiving today new or renewed interest in mathematical physics, in particular from the point of view of realising certain operators of interests self-adjointly.
  arXiv  Detail & Related papers  (2022-01-25T09:45:16Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)
• 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)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Relational observables, reference frames, and conditional probabilities [0.0]
  We show how conditional expectation values of worldline tensor fields are related to quantum averages of suitably defined relational observables. We analyze a recollapsing cosmological model, for which we construct unitarily evolving quantum relational observables.
  arXiv  Detail & Related papers  (2020-06-09T21:54:18Z)

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.