Synopsis
Seven years after the first experiments in the new field of Nuclear Physics, the Highly Relativistic Heavy Ion Physics, the Nato-Advanced- Study-Institute on the 'Particle Production in Highly Excited Matter' was held from July 12 till July 24, 1992, at Il Ciocco, Castelvecchio Pascoli, near Lucca in Italy. The school took place at a mo ment when intensive efforts are mounted by the scientific community of Relativistic Heavy Ion Physics to meet the extraordinary challenge of the new upcoming physics opportunities. The gold beams of 10 GeV A at Brookhaven AGS have been sent to the experiments this Summer and we extent our congratulations to the persons and teams who made this possible. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven is under construction and expected to allow experiments to see collisions in the intersec tion regions early 1998. The lead beams at the SPS at CERN scheduled for summer 1994 are eagerly awaited by 6 large experiments, and many scientists are planning the experiments at the planned LHC with heavy ions to be turned on before the year 2000. Seen against this background of rather fierce activity, we were most delighted when NATO accepted our application for an Advanced Study Institute oriented to the main subject of this young and dynamic field of research. We are very grateful to the Scientific Affairs Division of NATO and Dr. L. DaCunha, the director of the Advanced Study Institute program for giving our community this opportunity.
About the Author
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
Johann Rafelski obtained his Ph.D. in 1973 and has been Professor of Physics at the University of Arizona since 1987. He teaches theoretical subatomic physics at both undergraduate and graduate level. Prior to this, he held a Chair at Theoretical Physics at University of Cape Town, and has been associate Professor of Theoretical Physics at University Frankfurt. He worked at the CERN laboratory in Geneva in various functions since 1977, and has been instrumental in the development of the relativistic heavy ion experimental program.
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