Wiener-Kolmogorov conception of the stochastic organization of nature by S. Molchanov The Wiener programme in statistical physics. Is it feasible in the light of recent developments? by O. Penrose The mathematical ramifications of Wiener's program in statistical physics by L. Gross Potential capacity before and after Wiener by D. R. Adams Generalized harmonic analysis and Gabor and wavelet systems by J. J. Benedetto Wiener-Hopf equations and linear systems by J. Bart, I. Gohberg, and M. A. Kaashoek Complex harmonic analysis in the aftermath of Paley-Wiener by P. Malliavin Amalgam spaces and generalized harmonic analysis by H. G. Feichtinger Wiener space and nonlinear quantum field theory by I. Segal Wiener and Feynman--path integrals and their applications by S. Albeverio Optical coherence before and after Wiener by J. R. Klauder Wiener and the problem of Hidden Parameters in quantum mechanics by E. A. Carlen Finite path integrals by E. F. Thomas Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory by R. L. Warnock The role of Leibniz and Haldane in Wiener's cybernetics by G. Gale Quantum mechanical coherence, resonance, and mind by H. P. Stapp What is mind that the brain may order it? by K. H. Pribram Shannon-Wiener information and stochastic complexity by J. Rissanen Sharp norm comparison of Martingale maximal functions and stochastic integrals by D. L. Burkholder Stochastic analysis on Wiener space by S. Watanabe Stochastic filtering: A part of stochastic nonlinear analysis by G. Kallianpur The theory of learning before and after Wiener by N. K. Bose Sensory and motor prostheses in the aftermath of Wiener by R. W. Mann On Wiener's thought in the computer as an aid in visualizing higher-dimensioanl forms and its modern ramifications by D. Roseman Norbert Wiener and the future of cybernetics by P. R. Masani Letter to Norbert Wiener from John von Neumann Scientific impact of the work of C. E. Shannon by B. McMillan Citation and award of the Norbert Wiener Centenary Medal to Professor C. E. Shannon (in absentia) by J. Ramaekers Wiener and the art of communication by D. Gabor Academic vita of Norbert Wiener Doctoral students of Norbert Wiener Bibliography of Norbert Wiener Defense Department documents List of participants (Norbert Wiener centenary congress).
Wiener-Kolmogorov conception of the stochastic organization of nature by S. Molchanov The Wiener programme in statistical physics. Is it feasible in the light of recent developments? by O. Penrose The mathematical ramifications of Wiener's program in statistical physics by L. Gross Potential capacity before and after Wiener by D. R. Adams Generalized harmonic analysis and Gabor and wavelet systems by J. J. Benedetto Wiener-Hopf equations and linear systems by J. Bart, I. Gohberg, and M. A. Kaashoek Complex harmonic analysis in the aftermath of Paley-Wiener by P. Malliavin Amalgam spaces and generalized harmonic analysis by H. G. Feichtinger Wiener space and nonlinear quantum field theory by I. Segal Wiener and Feynman--path integrals and their applications by S. Albeverio Optical coherence before and after Wiener by J. R. Klauder Wiener and the problem of Hidden Parameters in quantum mechanics by E. A. Carlen Finite path integrals by E. F. Thomas Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory by R. L. Warnock The role of Leibniz and Haldane in Wiener's cybernetics by G. Gale Quantum mechanical coherence, resonance, and mind by H. P. Stapp What is mind that the brain may order it? by K. H. Pribram Shannon-Wiener information and stochastic complexity by J. Rissanen Sharp norm comparison of Martingale maximal functions and stochastic integrals by D. L. Burkholder Stochastic analysis on Wiener space by S. Watanabe Stochastic filtering: A part of stochastic nonlinear analysis by G. Kallianpur The theory of learning before and after Wiener by N. K. Bose Sensory and motor prostheses in the aftermath of Wiener by R. W. Mann On Wiener's thought in the computer as an aid in visualizing higher-dimensioanl forms and its modern ramifications by D. Roseman Norbert Wiener and the future of cybernetics by P. R. Masani Letter to Norbert Wiener from John von Neumann Scientific impact of the work of C. E. Shannon by B. McMillan Citation and award of the Norbert Wiener Centenary Medal to Professor C. E. Shannon (in absentia) by J. Ramaekers Wiener and the art of communication by D. Gabor Academic vita of Norbert Wiener Doctoral students of Norbert Wiener Bibliography of Norbert Wiener Defense Department documents List of participants (Norbert Wiener centenary congress).
Feynman functional integrals and the stochastic limit, L. Accardi dynamical programming, filtering and control of quantum Markov processes, V.P. Belavkin quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrodinger equation, A.M. Chebotarev on phase transitions, M. Corgini existence of attractors for dissipative Schrodinger equation in R, M.A. Astaburuaga and V.H. Cortes reduction of noise by squeezed vacuum, F. Fagnola et al outgoing states and resonant behaviour, C. Fernandez stochastic Dyson series and the solution to associated stochastic evolution equations, G.W. Johnson and G. Kallianpur norm estimates for a class of semigroups of Schrodinger type, H. Prado on the recurrence of quantum dynamical semigroups, R. Rebolledo collective interactions in CQED, C. Saavedra T-product and Wiener Measure, D.P. Sankovich from Feynman-Kac formulae to Feynman-Kac semigroups, J.A. van Casteren completely positive quantum stochastic flows with infinite degrees of freedom, J. Lindsay and S.J. Wills characterization of continuous operators on infinite dimension distribution spaces, S.-L. Luo and J.-A. Yan a special time-dependent quantum invariant and a general theorem on quantum symmetries, J.-G. Zambrini.
How we, human being, have evolved to such complexity from nothing?, M. Oda why and how physicists are interested in brain and mind?, M. Oda a method for information analysis of sequences by two-dimensional pattern formation with colouration, N. Obata et al teleportation of general quantum states, L. Accardi and M. Ohya on acerain integral formula in stochastic analysis, I. Doku comments on Nelson's quantum stochastic process - tunnelling time and domain structure, T. Hashimoto some of future directions in white noise analysis, T. Hida quantum computer - an overview, A. Hosoya on the computational power of bounded error quantum turing machines, T. Nishino mutual entropy in quantum information and information genetics, M. Ohya the Levy Laplacian as a self-adjoint operator, K. Saito and A.H. Tsoi on variation theory of structures and Kiho's problem, Y. Shikata and M. Tsukamoto topics on random fields, (i Si), extracting order from chaotic world through perceptual grouping processes in human sensory system, N. Sugie models of quantum computers and decoherence problem, I.V. Volovich analysis and control of decoherence in spin system, M. Yamanoi.
Preface Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation L. Accardi and L. Y. Gang 2. Schrodinger operators with potentials supported by null sets S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom 3. Landau Hamiltonians on symmetric spaces J. E. Avron and A. Pnueli 4. Renormalization group analysis and quasicrystals J. Bellissard 5. The measurement problem in the stochastic formulation of quantum mechanics Ph. Blanchard, M. Cini and M. Serva 6. Schrodinger operators at threshold D. Bolle 7. Spectral analysis and scattering theory for Schrodinger operators with an interaction supported by a regular curve J. F. Brasche and A. Teta 8. Lattice models of solids V. V. Evstratov and B. S. Pavlov 9. Schrodinger operators on unusual manifolds P. Exner and P. Seba 10. High energy resolvent estimates for Schrodinger operators A. Jensen 11. Point interactions as solvable models W. Kirsch 12. Stochastic model of quantum mechanics V. P. Maslov Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Hoegh-Krohn's model of quantum fields S. Albeverio and S. Kusuoka 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems S. Albeverio and B. Zegarlinski 15. Hypercontractivity: a bibliographic review E. B. Davies, L. B. Gross and B. Simon 16. Progress and problems in algebraic quantum field theory S. Doplicher 17. Hoegh-Krohn's model of quantum fields and the absolute continuity of measures S. Kusuoka 18. Baryon states in lattice QCD R. A. Minlos and E. A. Zhinzhina 19. The energy of a Weyl soliton R. F. Streater Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model S. Albeverio, Ph. Blanchard, D. Gandolfo, R. Hoegh-Krohn and M. Mebkhout 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction R. L. Dobrushin and S. B. Shlosman 22. Verification of the global Markov property for strongly coupled trigonometric interactions R. Gielerak 23. Decomposition of Ising models and the Mayer expansion C. M. Newman and G. A. Baker, Jr 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics A. G. Shuhov, Yu. M. Suhov and A. V. Teslenko 25. Towards time-dynamics for bosonic systems in quantum statistical mechanics, 2 A. G. Shuhov and Yu. M. Suhov.
Some thoughts on the infinite dimensional harmonic analysis, T. Hida and Y.-H. Mimachi a quarter century of white noise theory, H.-H. Kuo the Clark formula of generalized Wiener functionals, Y.-J. Lee and H.-H. Shih a treatment of quantum Baker's map by chaos degree, K. Inoue et al inverse S-transform, Wick product and overcompleteness of exponential vectors, N. Obata a Hausdorff-Young inequality for white noise analysis, H.-H. Kuo et al integral transform and Segal-Bargmann representation associated to q-Charlier polynomials, N. Asai topics on complex Gaussian random fields, S. Si and W.W. Htay quantum information in space and time and theory of stochastic processes, I.V. Volovich notions of independence in algebraic probability theory and set partition statistics, Y. Hashimoto Poisson noise analysis based on the Levy Laplacian, A. Ishikawa et al study on the power of potential fluctuation in living cells, M. Yamanoi some properties of measure-valued processes with singular branching rate, I. Doku. (Part contents)
A Combinatorial Identity and Its Application to Gaussian Measure (L Accardi, H-H Kuo & A I Stan) Integral Representation of Positive Operator on Infinite Dimensional Space of Entire Functions (W Ayed & H Ouerdiane) Comparison of Some Methods of Quantum State Estimation (D Petz et al.) Entropic Bounds and Continual Measurements (A Barchielli & G Lupieri) Covariant Quantum Stochastic Flows and Their Dilation (V Belavkin & L Gregory) Alicki-Fannes and Hudson-Parthasarathy Evolution Equations (A C R Belton) Functional Integrals Over Smolyanov Surface Measures for Evolution Equations in a Riemannian Manifold (Ya A Butko) Quantum Probabilistic Model for the Financial Market (O Choustova) Note on the Time Operator (T Hida) An Analytic Double Product Integral (R L Hudson) To Quantum Mechanics Through Gaussian Integration and the Taylor Expansion of Functionals of Classical Fields (A Yu Khrennikov) A Theorem on Liftings of Statistical Operators (J Kupsch) Thermodynamical Formalism for Quasi-Local C*-Systems and Fermion Grading Symmetry (H Moriya) Micro-Macro Duality and an Attempt Towards Measurement Scheme of Quantum Fields (I Ojima) The Levy Laplacian Acting on Some Class of Levy Functionals (K Saito & A H Tsoi) On the General Form of the Integral-Sigma Lemma in Symmetric Fock Space (K Schubert) Spatial E0-Semigroups are Restrictions of Inner Automorphism Groups (M Skeide) A Characterization of Poisson Noise (Si Si) On Two Conjectures in Segal-Bargmann Analysis (S B Sontz) Note on Quantum Mutual Type Entropies and Capacity (N Watanabe) and other papers.
Introduction Preliminary remarks The path integral formalism is one of the most important tools in modern theoretical physics. Integration in functional spaces was considered for the first time by Norbert Wiener in his studies of diffusion processes [60, 61]. The corresponding integration measure is now known as the Wiener measure, i.e. the so-called Gaussian path integrals were studied. In quantum mechanics, functional integrals were introduced by R. Feynmann [62, 63] who was inspired by important observations due to P. A. M. Dirac concerning a relation between wave function and classical action [64, 65]. In modern physics the path integral formalism is applied not only to developing a quantum description for systems with infinitely many degrees of freedom as, for example, in quantum field theories or condensed matter physics, but also to ordinary quantum mechanical problems. Moreover there is a tendency to reformulate standard quantum mechanical problems (such as a particle in a “box” or potential well [66, 67], or a particle in the Coulomb field [68]) within the framework of the path integral method. The reason for doing this is rather obvious: physicists develop a new mathematical tool, a new language and, in order to comprehend all of its subtleties, it is necessary to investigate as many concrete examples as possible. Use of the path integral formalism is widespread in quantum field theory because it is the most adequate mathematical tool for a wide range of problems which allows, not only for elegant formulation of problems, but also for a great deal of simplification of their theoretical analysis.