Spectral Action in Noncommutative Geometry

Spectral Action in Noncommutative Geometry

Iochum, Bruno; Eckstein, Michal

Springer International Publishing AG

10/2018

155

Mole

Inglês

9783319947877

Pré-lançamento - envio 15 a 20 dias após a sua edição

This book offers a guided tour through the mathematical habitat of noncommutative geometry a la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given.
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.