Simplicial Quantum Gravity and Random Lattices

Abstract

Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus - dynamical triangulations 3. Two dimensional quantum gravity, dynamical triangulations and matrix models continuum formulation - dynamical triangulations and continuum limit - one matrix model - various matrix models - numerical studies - c=1 barrier - intrinsic geometry of 2d gravity - Liouville at c>25 4. Euclidean quantum gravity in three and four dimensions what are we looking for? - 3d simplicial gravity - 4d simplicial gravity - 3d and 4d Regge calculus 5. Non-perturbative problems in two dimensional quantum gravity double scaling limit - string equation - non-perturbative properties of the string equation - divergent series and Borel summability - non-perturbative effects in 2d gravity and string theories - stabilization proposals 6. Conclusion

(Lectures given at Les Houches Summer School, July 1992) 63 pages, plain TeX (foreword) + uuencoded tar-compressed PostScript file (main text + figures)

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• Lattices and Their Continuum Limits
• Noncommutative Lattices and Their Continuum Limits
• Expanding Polyhedral Universe in Regge Calculus
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