Random Surfaces and Quantum Gravity: International Proceedings: 262 (NATO Science Series B: Physics) - Hardcover

Hardcover

ISBN 10: 0306439395 ISBN 13: 9780306439391

Publisher: Kluwer Academic / Plenum Publishers, 1991

Synopsis

2D Gravity and Non-Perturbative Effects: Diffusion Equation, Continuum Limit and Universality in 2D Quantum Gravity; O. Alvarez, et al. On Triangles and Squares; C. Bachas. Non-Perturbative Effects in 2D Gravity and Matrix Modles; F. David. Integrable Models of 2D Quantum Gravity; P. Di Francesco, et al. Topological Strings and Loop Equations; R. Dijkgraaf, et al. The Two Matrix Model; M.R. Douglas. Action Principle and Large Order Behavior of Non-Perturbative Gravity; P. Ginsparg, et al. D = 1 Strings and String Field Theory: Matrix Models, String Field Theory and Topology; T. Banks. Multipoint Correlation Functions in One-Dimensional String Theory; D. Boulativ. The Penner Model and D = 1 String Theory J. Distler, et al. Non-Perturbative String Theory; D.J. Gross. Bosonic Strings and String Field Theories in One-Dimensional Target Space; V. Kazakov. Liouville Theory andD 1: Random Surfaces in Dimensions Larger than One; J. Ambjorn. On Gauge Invariances in Stochastic Quantization; L. Baulieu. The Quantum Group Structure of Quantum Gravity in Two Dimensions; J.L. Gervais. Notes on Quantum Liouville Theory and Quantum Gravity; N. Seiberg. 8 additional articles. Index.

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Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index

Synopsis

Methods on the random triangulations of surfaces provide a description of non-critical string theory or equivalently of the coupling of matter fields to quantum gravity in two dimensions. Among the papers presented at the Cargese meeting are detailed reviews that make the volume useful for the non-specialist. Three main themes are treated extensive

Edition details

• Publisher: Kluwer Academic / Plenum Publishers
• Publication date: 1991
• Language: English
• ISBN 10: 0306439395
• ISBN 13: 9780306439391
• Binding: Hardcover
• Number of pages: 406
• Editor: Alvarez Orlando, Etc.