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Books > Science & Mathematics > Physics > Relativity physics
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Colored Discrete Spaces - Higher Dimensional Combinatorial Maps and Quantum Gravity (Paperback, Softcover reprint of the original 1st ed. 2018)
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Colored Discrete Spaces - Higher Dimensional Combinatorial Maps and Quantum Gravity (Paperback, Softcover reprint of the original 1st ed. 2018)
Series: Springer Theses
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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.
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