04591nam 22007095 450 991030344030332120200706051652.03-319-94788-510.1007/978-3-319-94788-4(CKB)4100000007223654(MiAaPQ)EBC5622481(DE-He213)978-3-319-94788-4(PPN)232965463(EXLCZ)99410000000722365420181218d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierSpectral Action in Noncommutative Geometry /by Michał Eckstein, Bruno Iochum1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (165 pages)SpringerBriefs in Mathematical Physics,2197-1757 ;273-319-94787-7 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. .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 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 serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.SpringerBriefs in Mathematical Physics,2197-1757 ;27PhysicsMathematical physicsParticles (Nuclear physics)Quantum field theoryGravitationGeometry, AlgebraicHarmonic analysisMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Elementary Particles, Quantum Field Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P23029Classical and Quantum Gravitation, Relativity Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P19070Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Abstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Physics.Mathematical physics.Particles (Nuclear physics)Quantum field theory.Gravitation.Geometry, Algebraic.Harmonic analysis.Mathematical Methods in Physics.Mathematical Physics.Elementary Particles, Quantum Field Theory.Classical and Quantum Gravitation, Relativity Theory.Algebraic Geometry.Abstract Harmonic Analysis.515.7222Eckstein Michałauthttp://id.loc.gov/vocabulary/relators/aut1059670Iochum Brunoauthttp://id.loc.gov/vocabulary/relators/autBOOK9910303440303321Spectral Action in Noncommutative Geometry2507533UNINA