Continuum canonical purifications

• URL: http://arxiv.org/abs/2512.17014v2
• Date: Mon, 22 Dec 2025 22:54:27 GMT
• Title: Continuum canonical purifications
• Abstract summary: Given a state on a $*$-algebra, the canonical purification is a state on a "doubled" algebra that admits an interpretation in terms of CRT reflection.<n>We then identify conditions under which canonical purifications are "pure" in the technical sense, compute their modular conjugations, and relate them to GNS and natural-cone purifications in certain settings.<n>In an appendix, we develop a general theory of von Neumann algebras generated by $*$-algebras.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct and characterize canonical purifications for general algebraic states, extending prior constructions by Woronowicz and by Dutta/Faulkner to general quantum theories. Given a state on a $*$-algebra, the canonical purification is a state on a "doubled" algebra that admits an interpretation in terms of CRT reflection. This interpretation holds for all quantum theories, even in the absence of gravity. We then identify conditions under which canonical purifications are "pure" in the technical sense, compute their modular conjugations, and relate them to GNS and natural-cone purifications in certain settings. In an appendix, we develop a general theory of von Neumann algebras generated by unbounded $*$-algebras. In a forthcoming paper with Caminiti and Capeccia, we provide an application of this general theory to the problem of excitability in quantum field theory.

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