LEADER 04591nam 22007095 450 001 9910303440303321 005 20200706051652.0 010 $a3-319-94788-5 024 7 $a10.1007/978-3-319-94788-4 035 $a(CKB)4100000007223654 035 $a(MiAaPQ)EBC5622481 035 $a(DE-He213)978-3-319-94788-4 035 $a(PPN)232965463 035 $a(EXLCZ)994100000007223654 100 $a20181218d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpectral Action in Noncommutative Geometry /$fby Micha? Eckstein, Bruno Iochum 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (165 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v27 311 $a3-319-94787-7 327 $aPreface -- 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. . 330 $aWhat is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry ŕ la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v27 606 $aPhysics 606 $aMathematical physics 606 $aParticles (Nuclear physics) 606 $aQuantum field theory 606 $aGravitation 606 $aGeometry, Algebraic 606 $aHarmonic analysis 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 615 0$aPhysics. 615 0$aMathematical physics. 615 0$aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 0$aGravitation. 615 0$aGeometry, Algebraic. 615 0$aHarmonic analysis. 615 14$aMathematical Methods in Physics. 615 24$aMathematical Physics. 615 24$aElementary Particles, Quantum Field Theory. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aAlgebraic Geometry. 615 24$aAbstract Harmonic Analysis. 676 $a515.7222 700 $aEckstein$b Micha?$4aut$4http://id.loc.gov/vocabulary/relators/aut$01059670 702 $aIochum$b Bruno$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910303440303321 996 $aSpectral Action in Noncommutative Geometry$92507533 997 $aUNINA