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Type III σ-spectral triples and quantum statistical mechanical systems

Greenfield, Mark and Marcolli, Matilde and Teh, Kevin (2013) Type III σ-spectral triples and quantum statistical mechanical systems. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170712-132224908

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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 type III σ-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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1305.5492arXivDiscussion Paper
Additional Information:(Submitted on 23 May 2013). The first author was supported for this work by a Summer Undergraduate Research Fellowship at Caltech. The second author is partially supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The second author thanks MSRI for hospitality and support.
Funders:
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
NSFDMS-0901221
NSFDMS-1007207
NSFDMS-1201512
NSFPHY-1205440
Mathematical Sciences Research Institute (MSRI)UNSPECIFIED
Record Number:CaltechAUTHORS:20170712-132224908
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170712-132224908
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79016
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jul 2017 21:26
Last Modified:12 Jul 2017 21:26

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