Spectral Action in Noncommutative Geometry

Spectral Action in Noncommutative Geometry

Iochum, Bruno; Eckstein, Michal

Springer International Publishing AG

01/2019

155

Mole

Inglês

9783319947877

15 a 20 dias

454

Descrição não disponível.
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.
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