Current Topics in Astrofundamental Physics: Primordial Cosmology - Nato Science Series C

Marc Notes: Includes bibliographical references and index.; Proceedings of the NATO Advanced Study Institute on Current Topics in Astrofundamental Physics: Primordial Cosmology, Erice, Italy, 4-15 September 1997--T.p. verso.; Published in cooperation with NATO Scientific Affairs Division.. Table of Contents: Preface. I: The Early Universe. Covariant Analysis of Dynamics and of CBR Anisotropy; G. F. R. Ellis, P. K. S. Dunsby. Recent Progress in String Cosmology; N. Sanchez. Reheating in Inflationary Cosmology; A. Linde. Out of Equilibrium Fields in Inflationary Dynamics. Density Fluctuations; D. Boyanovsky, et al. Kinetic Theory of Hot Gauge Theories: Overview, Details & Extensions; R. D. Pisarski. Electroweak Phase Transition in the Early Universe? B. Bergerhoff, C. Wetterich. Limits on Cosmological Magnetic Fields and Other Anisotropic Stresses; J. D. Barrow. Varying G and Other Constants; J. D. Barrow. II: Cosmic Microwave Background Radiation. Cosmic Microwave Background Anisotropy Science; G. F. Smoot. The Cosmic Microwave Background; A. N. Lasenby, A. W. Jones. Spectrum of the Cosmic Microwave Background: Results and Prospects; A. Kogut. Large-Scale Anisotropy of the Cosmic Microwave Background; A. Kogut. Recent Developments in the Calculation of CMB Anisotropies; A. D. Challinor, A. N. Lasenby. Dark Ages' of the Universe; Y. Parijskij, et al. III: Large Scale Structure, Dark Matter. Status of Cosmological Parameters; J. R. Primack. The Direct Detection of Dark Matter; B. Sadoulet. Signatures of Quantum Gravity in the Large-Scale Universe; L. P. Grishchuk. Tidal Interaction of a Star with a Supermassive Black Hole; I. D. Novikov. IV: Fractals and Scaling Laws in Astrophysics and Cosmology. Correlations Associated with Critical Phenomena; H. E. Stanley. Fractality, Lacunarity, and the Near-Isotropic Distribution of Galaxies; B. B. Mandelbrot. Correlation Properties of the Large Scale Matter Distribution and Galaxy Number Counts; L. Pietronero, et al. Fractal Dimensions and Scaling Laws in the Interstellar Medium and Galaxy Distributions: A New Field Theory Approach; H. J. de Vega, et al. V: Neutrinos in Astrophysics. Neutrino Cosmology; A. D. Dolgov. Solar and Supernova Constraints on Cosmologically Interesting Neutrinos; W. C. Haxton. Photographs of the Institute. Author Index. Publisher Marketing: This NATO Advanced Study Institute course provided an updated understanding, from a fundamental and deep point of view, of the progress and current problems in the early universe, cosmic microwave background radiation, large-scale struc ture, dark matter problem, and the interplay between them. Emphasis was placed on the mutual impact of fundamental physics and cosmology, both at the theo retical and experimental or observational levels, within a deep and well defined programme, and a global unifying view, which, in addition, provides of careful inter-disciplinarity. In addition, each course of this series introduced and promoted topics or sub jects which, although not of a purely astrophysical or cosmological nature, were of relevant physical interest for astrophysics and cosmology. Deep understanding, clarification, synthesis, and careful interdisciplinarity within a fundamental physics framework, were the main goals of the course. Lectures ranged from a motivation and pedagogical introduction for students and participants not directly working in the field to the latest developments and most recent results. All lectures were plenary, had the same duration, and were followed by a discus sion. The course brought together experimentalists and theoreticans physicists, astro physicists and astronomers from a wide variety of backgrounds, including young scientists at the post-doctoral level, senior scientists and advanced graduate stu dents as well."

Contributor Bio:  North Atlantic Treaty Organization 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