Geometric Phases Characterise Operator Algebras and Missing Information

• URL: http://arxiv.org/abs/2306.00055v2
• Date: Tue, 3 Oct 2023 21:14:32 GMT
• Title: Geometric Phases Characterise Operator Algebras and Missing Information
• Authors: Souvik Banerjee, Moritz Dorband, Johanna Erdmenger, Anna-Lena Weigel
• Abstract summary: We show how geometric phases may be used to fully describe quantum systems, with or without gravity. We find a direct relation between geometric phases and von Neumann algebras.
• Score: 0.6749750044497732
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show how geometric phases may be used to fully describe quantum systems, with or without gravity, by providing knowledge about the geometry and topology of its Hilbert space. We find a direct relation between geometric phases and von Neumann algebras. In particular, we show that a vanishing geometric phase implies the existence of a well-defined trace functional on the algebra. We discuss how this is realised within the AdS/CFT correspondence for the eternal black hole. On the other hand, a non-vanishing geometric phase indicates missing information for a local observer, associated to reference frames covering only parts of the quantum system considered. We illustrate this with several examples, ranging from a single spin in a magnetic field to Virasoro Berry phases and the geometric phase associated to the eternal black hole in AdS spacetime. For the latter, a non-vanishing geometric phase is tied to the presence of a centre in the associated von Neumann algebra.

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