Academic Journal
Geometric phases characterise operator algebras and missing information.
| Title: | Geometric phases characterise operator algebras and missing information. |
|---|---|
| Authors: | Banerjee, Souvik, Dorband, Moritz, Erdmenger, Johanna, Weigel, Anna-Lena |
| Source: | Journal of High Energy Physics; Oct2023, Vol. 2023 Issue 10, p1-46, 46p |
| 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. [ABSTRACT FROM AUTHOR] |
| Subject Terms: | GEOMETRIC quantum phases, OPERATOR algebras, VON Neumann algebras, HILBERT space, BLACK holes, ETERNITY |
| People: | VON Neumann, John, 1903-1957 |
| Copyright of Journal of High Energy Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| ISSN: | 11266708 |
| DOI: | 10.1007/JHEP10(2023)026 |
| Database: | Complementary Index |