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Functional Integration

Basics and Applications

  • Book
  • © 1997

Overview

Editors:
  1. Cecile DeWitt-Morette

    1. The University of Texas at Austin, Austin, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Pierre Cartier

    1. Ecole Normale Supérieure, Paris, France

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    You can also search for this editor in PubMed   Google Scholar

  3. Antoine Folacci

    1. Université de Corse, Corte, France

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Part of the book series: NATO Science Series B: (NSSB, volume 361)

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-x
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  2. A Rigorous Mathematical Foundation of Functional Integration

    1. A Rigorous Mathematical Foundation of Functional Integration

      • P. Cartier, C. DeWitt-Morette
      Pages 1-50

  3. Physics on and near Caustics

    1. Physics on and near Caustics

      • C. DeWitt-Morette, P. Cartier
      Pages 51-66

  4. Quantum Equivalence Principle

    1. Quantum Equivalence Principle

      • H. Kleinert
      Pages 67-92

  5. Variational Perturbation Theory for Path Integrals

    1. Variational Perturbation Theory for Path Integrals

      • H. Kleinert
      Pages 93-95

  6. Functional Integration and Wave Propagation

    1. Functional Integration and Wave Propagation

      • S. K. Foong
      Pages 97-130

  7. Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms

    1. Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms

      • A. Sokal
      Pages 131-192

  8. Path Integral Simulation of Long-Time Dynamics in Quantum Dissipative Systems

    1. Path Integral Simulation of Long-Time Dynamics in Quantum Dissipative Systems

      • Nancy Makri
      Pages 193-211

  9. Développements Récents sur les Groupes de Tresses Applications à la Topologie et à l’Algèbre

    1. Développements Récents sur les Groupes de Tresses Applications à la Topologie et à l’Algèbre

      • P. Cartier
      Pages 213-246

  10. An Introduction to Knot Theory and Functional Integrals

    1. An Introduction to Knot Theory and Functional Integrals

      • L. Kauffman
      Pages 247-308

  11. Locally Self-Avoiding Walks

    1. Locally Self-Avoiding Walks

      • D. Iagolnitzer, J. Magnen
      Pages 309-325

  12. Gauge Theory without Ghosts

    1. Gauge Theory without Ghosts

      • B. DeWitt, C. Molina-París
      Pages 327-361

  13. Localization and Diagonalization: A Review of Functional Integral Techniques for Low-Dimensional Gauge Theories and Topological Field Theories

    1. Localization and Diagonalization: A Review of Functional Integral Techniques for Low-Dimensional Gauge Theories and Topological Field Theories

      • M. Blau, G. Thompson
      Pages 363-410

  14. Participants Contributions by Title and Abstract

    1. Front Matter

      Pages 411-411
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    2. A Constructive Analog of Zimmermann’s Formula

      • Abdelmalek Abdesselam
      Pages 413-413

    3. Heat Kernel as the Basis for the Functional Integration in Quantum Field Theory

      • Ivan G. Avramidi
      Pages 413-413

    4. Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac Formula

      • Bernhard Bodmann, Simone Warzel
      Pages 414-414

    5. Anomalies in Brst Anti Brst Approach as a Functional Integration Problem

      • Violeta Calian
      Pages 414-414

    6. Semiclassical Approximation Using Wiener Measure

      • Fabienne Castell
      Pages 415-415

    7. Open Problem: The Measure for the Functional Integral

      • Bryce DeWitt
      Pages 415-415
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Keywords

About this book

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

Editors and Affiliations

  • The University of Texas at Austin, Austin, USA

    Cecile DeWitt-Morette

  • Ecole Normale Supérieure, Paris, France

    Pierre Cartier

  • Université de Corse, Corte, France

    Antoine Folacci

Bibliographic Information

  • Book Title: Functional Integration

  • Book Subtitle: Basics and Applications

  • Editors: Cecile DeWitt-Morette, Pierre Cartier, Antoine Folacci

  • Series Title: NATO Science Series B:

  • DOI: https://doi.org/10.1007/978-1-4899-0319-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-306-45617-6Published: 30 September 1997

  • Softcover ISBN: 978-1-4899-0321-1Published: 12 June 2013

  • eBook ISBN: 978-1-4899-0319-8Published: 11 November 2013

  • Series ISSN: 0258-1221

  • Edition Number: 1

  • Number of Pages: X, 431

  • Topics: Theoretical, Mathematical and Computational Physics, Physical Chemistry

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