Spectral Action in Noncommutative Geometry
What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral appro...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2018, 2018
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| Edition: | 1st ed. 2018 |
| Series: | SpringerBriefs in Mathematical Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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.