Lecture Notes in Physics

Quantum Triangulations

Moduli Spaces, Strings, and Quantum Computing

Authors: Carfora, Mauro, Marzuoli, Annalisa

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  • First self-contained exposition of the subject matter
  • Suitable for graduate students and specialists alike
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About this book

Research 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.  

Reviews

“At several place in mathematics triangulations of 2-manifolds are useful. … It is the goal of this book to give an access to these very interesting applications and relations. … The book makes an inspiring reading for mathematicians and theoretical physicists working in the field.” (Martin Schlichenmaier, zbMATH, Vol. 1326.81003, 2016)

“In this book, the authors present to the readers the rich structures underlying polyhedral surfaces. They discuss their relations with Riemann moduli spaces, noncritical string theory and quantum computing. … This book is a useful resource for mathematicians and physicists working in the field of quantum geometry, three-manifold invariants and string theory.” (Lee-Peng Teo, Mathematical Reviews, January, 2013)


Table of contents (6 chapters)

  • Triangulated Surfaces and Polyhedral Structures

    Carfora, Mauro (et al.)

    Pages 1-54

  • Singular Euclidean Structures and Riemann Surfaces

    Carfora, Mauro (et al.)

    Pages 55-81

  • Polyhedral Surfaces and the Weil–Petersson Form

    Carfora, Mauro (et al.)

    Pages 83-114

  • The Quantum Geometry of Polyhedral Surfaces

    Carfora, Mauro (et al.)

    Pages 115-174

  • State Sum Models and Observables

    Carfora, Mauro (et al.)

    Pages 175-216

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-24440-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-24439-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Triangulations
Book Subtitle
Moduli Spaces, Strings, and Quantum Computing
Authors
Series Title
Lecture Notes in Physics
Series Volume
845
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-24440-7
DOI
10.1007/978-3-642-24440-7
Softcover ISBN
978-3-642-24439-1
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XVII, 284
Number of Illustrations and Tables
80 b/w illustrations, 10 illustrations in colour
Topics