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010   $a3-319-96023-7
024 7 $a10.1007/978-3-319-96023-4
035   $a(CKB)4100000005471793
035   $a(DE-He213)978-3-319-96023-4
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035   $a(PPN)229915396
035   $a(EXLCZ)994100000005471793
100   $a20180801d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aColored Discrete Spaces $eHigher Dimensional Combinatorial Maps and Quantum Gravity /$fby Luca Lionni
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XVIII, 218 p. 107 illus., 98 illus. in color.) 
225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053
311   $a3-319-96022-9 
320   $aIncludes bibliographical references at the end of each chapters.
327   $aColored Simplices and Edge-Colored Graphs -- Bijective Methods -- Properties of Stacked Maps -- Summary and Outlook.
330   $aThis book provides a number of combinatorial tools that allow a systematic study of very general discrete spaces involved in the context of discrete quantum gravity. In any dimension D, we can discretize Euclidean gravity in the absence of matter over random discrete spaces obtained by gluing families of polytopes together in all possible ways. These spaces are then classified according to their curvature. In D=2, it results in a theory of random discrete spheres, which converge in the continuum limit towards the Brownian sphere, a random fractal space interpreted as a quantum random space-time. In this limit, the continuous Liouville theory of D=2 quantum gravity is recovered. Previous results in higher dimension regarded triangulations, converging towards a continuum random tree, or gluings of simple building blocks of small sizes, for which multi-trace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked two-dimensional discrete surfaces for the most general colored building blocks, and details how it can be used to classify colored discrete spaces according to their curvature. The way in which this combinatorial problem arrises in discrete quantum gravity and random tensor models is discussed in detail.
410  0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053
606   $aPhysics
606   $aGravitation
606   $aGeometry
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070
606   $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006
615  0$aPhysics.
615  0$aGravitation.
615  0$aGeometry.
615 14$aMathematical Methods in Physics.
615 24$aClassical and Quantum Gravitation, Relativity Theory.
615 24$aGeometry.
676   $a530.15
700   $aLionni$b Luca$4aut$4http://id.loc.gov/vocabulary/relators/aut$0833960
906   $aBOOK
912   $a9910300542803321
996   $aColored Discrete Spaces$92523331
997   $aUNINA