Foundations of quantum theory. From classical concepts to operator algebras
type: Item
instance of: scholarly article
title: Foundations of quantum theory. From classical concepts to operator algebras
zbMATH Open document ID: 1380.81028
DOI: 10.1007/978-3-319-51777-3
published in: Fundamental Theories of Physics
publication date: 2017-05-17T00:00:00Z
review text: The stated aim of this ambitious new book -- which hence ranks it within the time honored field of the foundations of quantum mechanics -- ``is to analyze the foundations of quantum theory from the point of view of classical-quantum duality, using the mathematical formalism of operator algebras on Hilbert space'' (p. viii), the final target being even more aspiring: ``although experiments and detailed theoretical models are lacking so far, this powerful combination of mathematical and philosophical tools leads to a compelling scenario for solving the measurement problem, harboring the hope of finally laying this problem to rest'' (p. 14). This is distinctly commendable indeed because in so doing the book openly challenges the ``unfortunate `shut up and calculate' attitude most physicists seem to have (especially towards the measurement problem)'' (p. 435). According to this program the framework of \(C^*\)-algebras is adopted here in order to exploit the unification they provide of the commutative and the noncommutative worlds into a single mathematical scheme: a choice deemed unavoidable since some physical systems admit a dual description in either classical or quantum-mechanical terms, and in particular the measurement problem of quantum mechanics is supposed to be entailed precisetly by this duality. The development of the quantum theory in the first four decades of the XX century make clear that this unified language smooths the way for the required shifts between classical and quantum-mechanical modes of description which lies at the heart of the foundations of quantum physics: ``this `change of perspective', which roughly speaking amounts to switching (and interpolating) between commutative and noncommutative \(C^*\)-algebras, is added to Dirac's transformation theory (which comes down to switching between generalized bases, or, equivalently, between maximal commutative von Neumann algebras)'' (p. 3) The setting of the book however is admittedly rather philos…
reviewed by: Nicola Cufaro Petroni
Mathematics Subject Classification ID: 81P05
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 00A79
zbMATH DE Number: 6718357
zbMATH Keywords: \(C^*\)-algebras
zbMATH Keywords: foundations of quantum mechanics
zbMATH Keywords: quantum measurement theory
author: Klaas Landsman
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-51777-3
OpenAlex ID: W4213113249
description: scientific article; zbMATH DE number 6718357