rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Quantum Triangulations
    sub title: Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow
  name:
    name part: Carfora, Mauro.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Marzuoli, Annalisa.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    edition: 2nd ed. 2017.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 392 p. 113 illus., 92 illus. in color. online resource.
  abstract: This 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…
  table of contents: Preface -- 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.
  note: by Mauro Carfora, Annalisa Marzuoli.
  subject:
    topic: Physics
  subject:
    topic: Mathematical physics
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Complex manifolds
  subject:
    topic: Gravitation
  subject:
    topic: Quantum physics
  subject:
    topic: Physics
  subject:
    topic: Quantum Physics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Manifolds and Cell Complexes (incl. Diff.Topology)
  subject:
    topic: Classical and Quantum Gravitation, Relativity Theory
  subject:
    topic: Mathematical Applications in the Physical Sciences
  subject:
    topic: Numerical and Computational Physics, Simulation
  classification: QC173.96-174.52
  classification: 530.12
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Physics, 942
  identifier: 9783319679372
  identifier: http://dx.doi.org/10.1007/978-3-319-67937-2
  record info:
    record creation date: 171127
    record change date: 20171127151439.0
    record identifier: 978-3-319-67937-2