Spectral Action in Noncommutative Geometry

• Main Authors: Eckstein, Michał (Author, http://id.loc.gov/vocabulary/relators/aut), Iochum, Bruno (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: SpringerBriefs in Mathematical Physics, 27
• Subjects: Physics.; Mathematical physics.; Elementary particles (Physics).; Quantum field theory.; Gravitation.; Algebraic geometry.; Harmonic analysis.; Mathematical Methods in Physics.; Mathematical Physics.; Elementary Particles, Quantum Field Theory.; Classical and Quantum Gravitation, Relativity Theory.; Algebraic Geometry.; Abstract Harmonic Analysis.

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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. .