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Twisted spectral triples and quantum statistical mechanical systems

Twisted spectral triples and quantum statistical mechanical systems Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of twisted spectral triple, introduced recently by Connes and Moscovici, provides a natural bridge between them. We investigate explicit examples, related to the Bost-Connes quantum statistical mechanical system and to Riemann surfaces and graphs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png P-Adic Numbers, Ultrametric Analysis, and Applications Springer Journals

Twisted spectral triples and quantum statistical mechanical systems

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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Pleiades Publishing, Ltd.
Subject
Mathematics; Algebra
ISSN
2070-0466
eISSN
2070-0474
DOI
10.1134/S2070046614020010
Publisher site
See Article on Publisher Site

Abstract

Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of twisted spectral triple, introduced recently by Connes and Moscovici, provides a natural bridge between them. We investigate explicit examples, related to the Bost-Connes quantum statistical mechanical system and to Riemann surfaces and graphs.

Journal

P-Adic Numbers, Ultrametric Analysis, and ApplicationsSpringer Journals

Published: May 7, 2014

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