Spectral Action in Noncommutative Geometry

Preface.- The dwelling of the spectral action.- The toolkit for computations.- Analytic properties of spectral functions.- Fluctuations of the spectral action.- Open problems.- Classical tool from geometry and analysis.- About "heat operators.- Definition of pdos, Sobolev spaces and a few spectral properties.- Complex parameter-dependent symbols and parametrix.- About e-t P as a pdo and about its kernel.- The small-t asymptotics of e-t P.- Meromorphic extensions of certain series and their residues.- Examples of spectral triples.- Spheres.- Tori.- Noncommutative tori.- Podle?s sphere.- Index.

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• Física relativística
• Gravidade
• Física Matemática
• A física quântica (mecânica quântica e teoria quântica de campos)
• Geometria algébrica
• Análise complexa, variáveis ??complexas

Spectral triples;Mellin transforms;action functional;noncommutative geometry;almost-commutative geometries;noncommutative integral;operator heat trace;Poisson summation formula;spectral functions;Heat operator;Noncommutative tori;Podles sphere;heat Kernel expansion;Sobolev space