Friday, May 24, 2013

1305.5492 (Mark Greenfield et al.)

Type III sigma-spectral triples and quantum statistical mechanical

Mark Greenfield, Matilde Marcolli, Kevin Teh
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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