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Lookup NU author(s): Dr James Waldron
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© The Author(s) 2024. We develop an operational framework, combining relativistic quantum measurement theory with quantum reference frames (QRFs), in which local measurements of a quantum field on a background with symmetries are performed relative to a QRF. This yields a joint algebra of quantum-field and reference-frame observables that is invariant under the natural action of the group of spacetime isometries. For the appropriate class of quantum reference frames, this algebra is parameterised in terms of crossed products. Provided that the quantum field has good thermal properties (expressed by the existence of a KMS state at some nonzero temperature), one can use modular theory to show that the invariant algebra admits a semifinite trace. If furthermore the quantum reference frame has good thermal behaviour (expressed in terms of the properties of a KMS weight) at the same temperature, this trace is finite. We give precise conditions for the invariant algebra of physical observables to be a type II1 factor. Our results build upon recent work of Chandrasekaran et al. (J High Energy Phys 2023(2): 1–56, 2023. arXiv:2206.10780), providing both a significant mathematical generalisation of these findings and a refined operational understanding of their model.
Author(s): Fewster CJ, Janssen DW, Loveridge LD, Rejzner K, Waldron J
Publication type: Article
Publication status: Published
Journal: Communications in Mathematical Physics
Year: 2025
Volume: 406
Online publication date: 18/12/2024
Acceptance date: 30/10/2024
Date deposited: 06/01/2025
ISSN (print): 0010-3616
ISSN (electronic): 1432-0916
Publisher: Springer Nature
URL: https://doi.org/10.1007/s00220-024-05180-7
DOI: 10.1007/s00220-024-05180-7
Data Access Statement: No datasets were generated or analysed in this work.
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