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The Geometry of Dynamical Triangulations
Jan AmbjornMauro CarforaAnnalisa Marzuoli
出版Springer Science & Business Media, 1997-09-18
主題Computers / Information TechnologyMathematics / Geometry / GeneralScience / Space Science / CosmologyScience / Physics / GravityScience / Physics / Mathematical & ComputationalScience / Physics / GeneralScience / Physics / Quantum TheoryScience / Waves & Wave MechanicsScience / Physics / Condensed Matter
ISBN35406333089783540633303
URLhttp://books.google.com.hk/books?id=9lYHWfzQmS0C&hl=&source=gbs_api
EBookSAMPLE
註釋The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.