2013/05/23 by Mark Greenfield, M. B. Greenfield, Greenfield, Mark +4
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1305.5492
LaTeX, 22 pages
arxiv created 2013/05/23 · openalex publication_date 2013/05/23 · arxiv updated 2013/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.