LEADER 04889nam 22008415 450 001 996466791303316 005 20200701003902.0 010 $a3-540-31522-5 024 7 $a10.1007/b104936 035 $a(CKB)1000000000231916 035 $a(DE-He213)978-3-540-31522-3 035 $a(SSID)ssj0000317936 035 $a(PQKBManifestationID)11240989 035 $a(PQKBTitleCode)TC0000317936 035 $a(PQKBWorkID)10295491 035 $a(PQKB)10119104 035 $a(MiAaPQ)EBC4975576 035 $a(Au-PeEL)EBL4975576 035 $a(CaONFJC)MIL140213 035 $a(OCoLC)1024261891 035 $a(PPN)123090997 035 $a(EXLCZ)991000000000231916 100 $a20100805d2005 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric and Topological Methods for Quantum Field Theory$b[electronic resource] /$fedited by Hernan Ocampo, Sylvie Paycha, Andrés Vargas 205 $a1st ed. 2005. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2005. 215 $a1 online resource (XV, 230 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v668 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-24283-X 327 $aKnot Invariants and Configuration Space Integrals (Christine Lescop) -- Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar) -- Introduction to String Compactification (Anamaria Font, Stefan Theisen) -- Index Theorems and Noncommutative Topology (Thierry Fack). 330 $aThis volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v668 606 $aPhysics 606 $aQuantum field theory 606 $aString theory 606 $aElementary particles (Physics) 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aDifferential geometry 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aQuantum Field Theories, String Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19048 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aPhysics. 615 0$aQuantum field theory. 615 0$aString theory. 615 0$aElementary particles (Physics). 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aDifferential geometry. 615 14$aMathematical Methods in Physics. 615 24$aQuantum Field Theories, String Theory. 615 24$aElementary Particles, Quantum Field Theory. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aDifferential Geometry. 676 $a530.15 702 $aOcampo$b Hernan$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aPaycha$b Sylvie$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aVargas$b Andrés$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466791303316 996 $aGeometric and topological methods for quantum field theory$9239592 997 $aUNISA