說明 
1 online resource (xviii, 218 pages) : illustrations (some color), digital ; 24 cm 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

text file PDF rda 
系列 
Springer theses, 21905053


Springer theses

附註 
Colored Simplices and EdgeColored Graphs  Bijective Methods  Properties of Stacked Maps  Summary and Outlook 

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 spacetime. 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 multitrace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked twodimensional 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 
Host Item 
Springer eBooks

主題 
Mathematical physics


Quantum gravity  Mathematics


Combinatorial analysis


Physics


Mathematical Methods in Physics


Classical and Quantum Gravitation, Relativity Theory


Geometry

Alt Author 
SpringerLink (Online service)

