LEADER 04918nam 22007695 450 001 996466690103316 005 20200703155627.0 010 $a3-642-24440-8 024 7 $a10.1007/978-3-642-24440-7 035 $a(CKB)3390000000021734 035 $a(SSID)ssj0000610678 035 $a(PQKBManifestationID)11381079 035 $a(PQKBTitleCode)TC0000610678 035 $a(PQKBWorkID)10639438 035 $a(PQKB)10951114 035 $a(DE-He213)978-3-642-24440-7 035 $a(MiAaPQ)EBC3070486 035 $a(PPN)159085071 035 $a(EXLCZ)993390000000021734 100 $a20120113d2012 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aQuantum Triangulations$b[electronic resource] $eModuli Spaces, Strings, and Quantum Computing /$fby Mauro Carfora, Annalisa Marzuoli 205 $a1st ed. 2012. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2012. 215 $a1 online resource (XVII, 284 p. 90 illus., 10 illus. in color.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v845 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-24439-4 320 $aIncludes bibliographical references and index. 327 $aTriangulated Surfaces and Polyhedral Structures -- Singular Euclidean Structures an Riemann Surfaces -- Polyhedral Surfaces and the Weil-Petersson Form -- The Quantum Geometry of Polyhedral Surfaces -- State Sum Models and Observables -- Combinatorial Framework for Topological Quantum Computing -- A Capsule of Moduli Space Theory -- Spectral Theory on Polyhedral Surfaces -- Index. 330 $aResearch on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment.   The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest.   This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.  . 410 0$aLecture Notes in Physics,$x0075-8450 ;$v845 606 $aPhysics 606 $aMathematical physics 606 $aQuantum physics 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aGravitation 606 $aPhysics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/P00002 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aManifolds and Cell Complexes (incl. 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