Journal ArticleDOI
General relativity without coordinates
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In this article, the authors developed an approach to the theory of Riemannian manifolds which avoids the use of co-ordinates, by approximating curved spaces by higher-dimensional analogs of polyhedra.Abstract:
In this paper we develop an approach to the theory of Riemannian manifolds which avoids the use of co-ordinates. Curved spaces are approximated by higher-dimensional analogs of polyhedra. Among the advantages of this procedure we may list the possibility of condensing into a simplified model the essential features of topologies like Wheeler’s wormhole and a deeper geometrical insight.read more
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Random-matrix theories in quantum physics : common concepts
TL;DR: A review of the development of random-matrix theory (RMT) during the last fifteen years is given in this paper, with a brief historical survey of the developments of RMT and of localization theory since their inception.
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Random Matrix Theories in Quantum Physics: Common Concepts
TL;DR: It is suggested that the current development of random-matrix theory signals the emergence of a new “statistical mechanics”: Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
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Spin foam models for quantum gravity
TL;DR: In this paper, the authors present a review of spin foam formulations of nonperturbative (background-independent) quantum gravity and define the Barrett-Crane model for four-dimensional gravity.
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Spectral geometry of singular Riemannian spaces
TL;DR: In this article, the authors consider the trace du noyau de la chaleur and the application of la methode de l'equation de la Chaleur to theoreme d'indice for the caracteristique d'Euler et des complexes signatures.
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Planar diagrams, two-dimensional lattice gravity and surface models
TL;DR: Some discrete lattice models for quantum two-dimensional euclidean gravity are shown to be equivalent to zero-dimensional planar field theories as mentioned in this paper, and a universal continuum limit exists for open surfaces, but not for closed ones.