Colored Discrete Spaces (eBook, PDF)
Luca Lionni
eBook, PDF

Colored Discrete Spaces (eBook, PDF)

Higher Dimensional Combinatorial Maps and Quantum Gravity

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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-tim...

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