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The Geometry of Dynamical Triangulations

  • Book
  • © 1997

Overview

Authors:
  1. Jan Ambjørn

    1. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

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  2. Mauro Carfora

    1. International School for Advanced Studies, SISSA-ISAS, Trieste, Italy

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  3. Annalisa Marzuoli

    1. Department of Nuclear and Theoretical Physics, University of Pavia, Pavia, Italy

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  • The book is a long-sought mathematical introduction to a rapid developing field.

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 50)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    Pages 1-16

  3. Triangulations

    Pages 17-37

  4. Dynamical Triangulations

    Pages 39-68

  5. Moduli Spaces for Dynamically Triangulated Manifolds

    Pages 69-94

  6. Curvature Assignments for Dynamical Triangulations

    Pages 95-124

  7. Entropy Estimates

    Pages 125-156

  8. Analytical vs. Numerical Data

    Pages 157-174

  9. Back Matter

    Pages 175-197
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About this book

The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula­ tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.

Authors and Affiliations

  • Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    Jan Ambjørn

  • International School for Advanced Studies, SISSA-ISAS, Trieste, Italy

    Mauro Carfora

  • Department of Nuclear and Theoretical Physics, University of Pavia, Pavia, Italy

    Annalisa Marzuoli

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