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arXiv · 1305.5492

Type III sigma-spectral triples and quantum statistical mechanical systems

Mark Greenfield·Matilde Marcolli·Kevin Teh
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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 sigma-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.

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Mark Greenfield, Matilde Marcolli, Kevin Teh. 2013-05-23. Type III sigma-spectral triples and quantum statistical mechanical systems. https://arxiv.org/abs/1305.5492

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