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Article

Towards a Measurement Theory for Off-Shell Quantum Fields

1
Research Origin for Dressed Photon, 3-13-19 Moriya-cho, Kanagawa-ku, Yokohama 221-0022, Japan
2
Graduate School of Informatics, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan
Academic Editor: Motoichi Ohtsu
Symmetry 2021, 13(7), 1183; https://doi.org/10.3390/sym13071183
Received: 1 June 2021 / Revised: 27 June 2021 / Accepted: 28 June 2021 / Published: 30 June 2021
(This article belongs to the Special Issue Quantum Fields and Off-Shell Sciences)
In this study, we develop quantum measurement theory for quantum systems described by C-algebras. This is the first step to establish measurement theory for interacting quantum fields with off-shell momenta. Unlike quantum mechanics (i.e., quantum systems with finite degrees of freedom), measurement theory for quantum fields is still in development because of the difficulty of quantum fields that are typical quantum systems with infinite degrees of freedom. Furthermore, the mathematical theory of quantum measurement is formulated in the von Neumann algebraic setting in previous studies. In the paper, we aim to extend the applicable area of quantum measurement theory to quantum systems described by C-algebras from a mathematical viewpoint, referring to the sector theory that is related to symmetry and based on the theory of integral decomposition of states. In particular, we define central subspaces of the dual space of a C-algebra and use them to define instruments. This attempt makes the connection between measurement theory and sector theory explicit and enables us to understand the macroscopic nature and the physical meaning of measurement. View Full-Text
Keywords: quantum measurement; C*-algebra; algebraic quantum field theory; local net; extension of local net; completely positive instrument; macroscopic distinguishability quantum measurement; C*-algebra; algebraic quantum field theory; local net; extension of local net; completely positive instrument; macroscopic distinguishability
MDPI and ACS Style

Okamura, K. Towards a Measurement Theory for Off-Shell Quantum Fields. Symmetry 2021, 13, 1183. https://doi.org/10.3390/sym13071183

AMA Style

Okamura K. Towards a Measurement Theory for Off-Shell Quantum Fields. Symmetry. 2021; 13(7):1183. https://doi.org/10.3390/sym13071183

Chicago/Turabian Style

Okamura, Kazuya. 2021. "Towards a Measurement Theory for Off-Shell Quantum Fields" Symmetry 13, no. 7: 1183. https://doi.org/10.3390/sym13071183

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