000 06048nam a22006735i 4500
001 978-3-319-67937-2
003 DE-He213
005 20210118130119.0
007 cr nn 008mamaa
008 171127s2017 gw | s |||| 0|eng d
020 _a9783319679372
_9978-3-319-67937-2
024 7 _a10.1007/978-3-319-67937-2
_2doi
050 4 _aQC173.96-174.52
072 7 _aPHQ
_2bicssc
072 7 _aSCI057000
_2bisacsh
072 7 _aPHQ
_2thema
082 0 4 _a530.12
_223
100 1 _aCarfora, Mauro.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Triangulations
_h[electronic resource] :
_bModuli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow /
_cby Mauro Carfora, Annalisa Marzuoli.
250 _a2nd ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXX, 392 p. 113 illus., 92 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v942
505 0 _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 σ 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.
520 _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.
650 0 _aQuantum physics.
650 0 _aMathematical physics.
650 0 _aManifolds (Mathematics).
650 0 _aComplex manifolds.
650 0 _aGravitation.
650 0 _aPhysics.
650 1 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aClassical and Quantum Gravitation, Relativity Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19070
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
650 2 4 _aNumerical and Computational Physics, Simulation.
_0http://scigraph.springernature.com/things/product-market-codes/P19021
700 1 _aMarzuoli, Annalisa.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319679365
776 0 8 _iPrinted edition:
_z9783319679389
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v942
856 4 0 _uhttps://doi.org/10.1007/978-3-319-67937-2
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c447263
_d447263
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/