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The Resource Quantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow, by Mauro Carfora, Annalisa Marzuoli, (electronic resource)

Quantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow, by Mauro Carfora, Annalisa Marzuoli, (electronic resource)

Creator
Author
Contributor
Summary
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 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
Language
eng
Work
Publication
Edition
2nd ed. 2017.
Extent
1 online resource (XX, 392 p. 113 illus., 92 illus. in color.)
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
Isbn
9783319679372
Instance
Label
Quantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow
Title
Quantum Triangulations
Title remainder
Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow
Statement of responsibility
by Mauro Carfora, Annalisa Marzuoli
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
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 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
Member of
http://library.link/vocab/creatorName
Carfora, Mauro
Dewey number
530.12
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • dh_gA0_qHv4
  • zUcZ4YITcYk
Image bit depth
0
LC call number
QC173.96-174.52
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
Marzuoli, Annalisa.
Series statement
Lecture Notes in Physics,
Series volume
942
http://library.link/vocab/subjectName
  • Quantum theory
  • Cell aggregation
  • Quantum Physics
  • Mathematical Physics
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Classical and Quantum Gravitation, Relativity Theory
  • Mathematical Applications in the Physical Sciences
  • Numerical and Computational Physics, Simulation
Label
Quantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow, by Mauro Carfora, Annalisa Marzuoli, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Edition
2nd ed. 2017.
Extent
1 online resource (XX, 392 p. 113 illus., 92 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783319679372
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-67937-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4340000000223428
  • (DE-He213)978-3-319-67937-2
  • (EXLCZ)994340000000223428
Label
Quantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow, by Mauro Carfora, Annalisa Marzuoli, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Edition
2nd ed. 2017.
Extent
1 online resource (XX, 392 p. 113 illus., 92 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783319679372
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-67937-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4340000000223428
  • (DE-He213)978-3-319-67937-2
  • (EXLCZ)994340000000223428

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