L Streit

G G Emch

G C Hegerfeldt

This volume contains contributions by friends, colleagues and associates of John R Klauder on the occasion of his 60th birthday. Klauder's scientific work embraces vast territories from quantum theories to general relativity, optics and chaotic dynamics. A recurrent theme in his research is the role played by coherent states, in particular, in connection with path integral formulations of quantization. Perhaps at a less lofty level, this concept has had at least two spectacular applications: as a powerful investigative tool in quantum optics and as a precursor to wavelets. In a different vein, Klauder also attacked specific, non-renormalizable but exactly soluble, hard-core models in field theory, where he uncovered what has since been called the Klauder phenomenon. The contributors to this volume represent the special brand of mathematicians and physicists John Klauder helped define throughout his seminal career in the industrial and academic worlds. Contents:Preface (J R Klauder)A Remark on a Connection of Return to Equilibrium and Multiple Ground States in Some Perturbed XY–Model (H Araki)Covariance Sub-Algebras Connected with Symmetry Groups of C∗öAlgebras (H J Borchers)Coherent-State Path-Integrals and Their Relations to Wavelets (B De Facio)Brownian Motion and Its Conditional Descendants (P Garbaczweski)Path Integrals and Network Quantum Numbers (R Gilmore and M Jeffery)Reckoning of the Besselian Path Integral (A Inomata)On Q-Analogs of Coherent States (M A Lohe & L C Biedenharn)Coherent States and Squeezed States, Supercoherent States and Supersqueezed States (M M Nieto)How to Generate Thermal Photons — On the Computer (M R Schroeder)A Local Quantum Theory Without Positive Energy Representations (R F Streater)Quantum Noise and Thermal Noise (H Umezawa)and other papers Readership: Physicists and mathematicians. keywords:

On Klauder's Path: A Field Trip

L Accardi

Si Si

H H Kuo

N Obata

K Saitô

The topics discussed in this book can be classified into three parts: (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. (ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called “generalized white noise functionals”, and sometimes “Hida distribution”. (iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume. Contents:General Theory of White Noise FunctionalsGaussian and Other ProcessesInfinite Dimensional Harmonic Analysis and Rotation GroupQuantum TheoryFeynman Integrals and Random FieldsVariational Calculus and Random FieldsApplication to Biology Readership: Graduate students and researchers in the fields of probability theory, functional analysis, statistics and theoretical physics. Keywords:White Noise;Gaussian;Brownian Motion;LÃ©vy Process;Canonical Representation;Stochastic Infinitesimal Equation;Generalized Functional;Innovation;Multiple Markov;Random FieldReviews:“This collection of papers is a tribute to one of the great researchers within stochastic analysis, Takeyuki Hida … An interesting appendix, however, is the collection of remarks at the end of the book … These remarks serve to put the various papers into perspective, and represent a valuable contribution.”Mathematical Reviews

Selected Papers of Takeyuki Hida

T Hida

J Potthoff

This proceedings contains articles on white noise analysis and related subjects. Applications in various branches of science are also discussed. White noise analysis stems from considering the time derivative of Brownian motion (“white noise”) as the basic ingredient of an infinite dimensional calculus. It provides a powerful mathematical tool for research fields such as stochastic analysis, potential theory in infinite dimensions and quantum field theory. Contents:Exponential Estimates of Large Devivation Type for Itô Processes in Hilbert Space (P L Chow)Multilevel Branching Systems (D A Dawson et al)White Noise Analysis - An Overview (T Hida and J Potthoff)Generalized Functionals on ( R∞, B∞, N∞ ) (K Itô)White Noise Analysis as a Tool in Computing Feynman Integrals (D C Khandeka)White Noise from a Hilbert Space Point of View (P A Meyer)Anticipating Stochastic Calculus and Applications (D Ocone)Hierarchy of Noise Production in Living Cells (F Oosawa)Linear Kernels Associated with Distributions of Stochastic Processes (W Smolenski)Positive Generalized Brownian Functionals (Y Yokoi)and others Readership: Mathematicians and mathematical physicists.

Mathematics and Applications

White Noise Analysis

L Streit

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