Overview
- Nominated as an outstanding Ph.D. thesis by the University of Paris-Sud, Orsay, France
- Clearly explained and including many pedagogical figures and new results
- Marks significant progress towards developing matrix models for tensor models and discrete quantum gravity
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (5 chapters)
Keywords
About this book
This book provides a number of combinatorial tools that allow a systematic study of very general discrete spaces involved in the context of discrete quantum gravity. In any dimension D, we can discretize Euclidean gravity in the absence of matter over random discrete spaces obtained by gluing families of polytopes together in all possible ways. These spaces are then classified according to their curvature. In D=2, it results in a theory of random discrete spheres, which converge in the continuum limit towards the Brownian sphere, a random fractal space interpreted as a quantum random space-time. In this limit, the continuous Liouville theory of D=2 quantum gravity is recovered.
Previous results in higher dimension regarded triangulations, converging towards a continuum random tree, or gluings of simple building blocks of small sizes, for which multi-trace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked two-dimensional discrete surfaces for the most general colored building blocks, and details how it can be used to classify colored discrete spaces according to their curvature. The way in which this combinatorial problem arrises in discrete quantum gravity and random tensor models is discussed in detail.
Authors and Affiliations
Bibliographic Information
Book Title: Colored Discrete Spaces
Book Subtitle: Higher Dimensional Combinatorial Maps and Quantum Gravity
Authors: Luca Lionni
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-3-319-96023-4
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-96022-7Published: 13 August 2018
Softcover ISBN: 978-3-030-07133-2Published: 12 January 2019
eBook ISBN: 978-3-319-96023-4Published: 01 August 2018
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: XVIII, 218
Number of Illustrations: 9 b/w illustrations, 98 illustrations in colour
Topics: Mathematical Methods in Physics, Classical and Quantum Gravitation, Relativity Theory, Geometry