LEADER 05979nam 22007695 450 001 996466830003316 005 20200706144415.0 010 $a3-319-67937-6 024 7 $a10.1007/978-3-319-67937-2 035 $a(CKB)4340000000223428 035 $a(DE-He213)978-3-319-67937-2 035 $a(MiAaPQ)EBC6307371 035 $a(MiAaPQ)EBC5579003 035 $a(Au-PeEL)EBL5579003 035 $a(OCoLC)1014066258 035 $a(PPN)221251243 035 $a(EXLCZ)994340000000223428 100 $a20171127d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantum Triangulations$b[electronic resource] $eModuli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow /$fby Mauro Carfora, Annalisa Marzuoli 205 $a2nd ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XX, 392 p. 113 illus., 92 illus. in color.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v942 311 $a3-319-67936-8 320 $aIncludes bibliographical references and index. 327 $aPreface -- Acknowledgements -- Triangulated Surfaces and Polyhedral Structures -- Singular Euclidean Structures and Riemann Surfaces -- Polyhedral Surfaces and the Weil-Petersson Form -- The Quantum Geometry of Polyhedral Surfaces: Non?Linear ? Model and Ricci Flow -- The Quantum Geometry of Polyhedral Surfaces: Variations on Strings and All That -- State Sum Models and Observables -- State Sum Models and Observables -- Combinatorial Framework for Topological Quantum Computing -- Appendix A: Riemannian Geometry -- Appendix B: A Capsule of Moduli Space Theory -- Appendix C: Spectral Theory on Polyhedral Surfaces -- Index. 330 $aThis book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic. Research on polyhedral manifolds often reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear. This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models? effective action to Perelman?s energy-functional. No other published account of this matter is so detailed and informative. This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its  applications. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v942 606 $aQuantum physics 606 $aMathematical physics 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aGravitation 606 $aPhysics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 615 0$aQuantum physics. 615 0$aMathematical physics. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aGravitation. 615 0$aPhysics. 615 14$aQuantum Physics. 615 24$aMathematical Physics. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aNumerical and Computational Physics, Simulation. 676 $a530.15 700 $aCarfora$b Mauro$4aut$4http://id.loc.gov/vocabulary/relators/aut$052579 702 $aMarzuoli$b Annalisa$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466830003316 996 $aQuantum Triangulations$92162701 997 $aUNISA