Buch, Englisch, Band 27, 155 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 271 g
Buch, Englisch, Band 27, 155 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 271 g
Reihe: SpringerBriefs in Mathematical Physics
ISBN: 978-3-319-94787-7
Verlag: Springer International Publishing
After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries.
The book servesboth as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Quantenphysik Teilchenphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Naturwissenschaften Physik Quantenphysik Relativität, Gravitation
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
Weitere Infos & Material
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.
