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Noncommutative geometry and quantum statistical mechanical systems

Aadne, Matthew Terje
Master thesis
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Year
2014
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http://urn.nb.no/URN:NBN:no-46645

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  • Anvendt matematikk og og mekanikk [234]
Abstract
In their paper, "Type III sigma-spectral triples and quantum statistical mechanical systems", M. Greenfield, M. Marcolli and K. Teh used the Bost-Connes system to construct a type III sigma-spectral triple where the twisting automorphism is a gauge automorphism. In this way they explored the link between quantum statistical mechanical systems and type III sigma-spectral triples. This thesis is dedicated to presenting their work pertaining to the Bost-Connes system, and to explore generalisations of their procedure. The text explores the possibilities for constructing type III sigma-spectral triples from lattice ordered semigroups and relating them to quantum statistical mechanical systems whose algebra of observables are semigroup crossed products.
 
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