The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics.
Contents: Quantization Techniques: A Quick Overview (S T Ali); The Quantum Geometer's Universe: Particles, Interactions and Topology (J Govaerts); Theoretical Methods of Modern Classical and Quantum Physics: Do Cross-Sections Determine Phase Shifts Uniquely? (D Atkinson); Hilbert Transform or Kramers-Kronig Relations Applied to Some Aspects of Linear and Nonlinear Physics (G Debiais); Application of the Gibbs Sampler to the Conditional Simulation of Rain Fields (H Onibon et al.); The Mathematics of an Algebraic Approach to the Physics of Hadrons (M D Slaughter); Coherent States, Wavelets and Geometric Methods in Theoretical Physics: Phase Space Geometry in Classical and Quantum Mechanics (J R Klauder); Functional Analysis Special Functions and Orthogonal Polynomials: On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One (E Azatassou & M N Hounkonnou); On a Generalization of the Method by Barbaroux et al. for the Improvement on the Rate of Decay of an Operator Resolvent (G Honnouvo & M N Hounkonnou); and other papers.