Functional Integration

Basics and Applications

  • Cecile DeWitt-Morette
  • Pierre Cartier
  • Antoine Folacci

Part of the NATO ASI Series book series (NSSB, volume 361)

Table of contents

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

    1. P. Cartier, C. DeWitt-Morette
      Pages 1-50
  3. Physics on and near Caustics

    1. C. DeWitt-Morette, P. Cartier
      Pages 51-66
  4. Quantum Equivalence Principle

    1. H. Kleinert
      Pages 67-92
  5. Variational Perturbation Theory for Path Integrals

  6. Functional Integration and Wave Propagation

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

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

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

  10. An Introduction to Knot Theory and Functional Integrals

  11. Locally Self-Avoiding Walks

    1. D. Iagolnitzer, J. Magnen
      Pages 309-325
  12. Gauge Theory without Ghosts

    1. 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

  14. Participants Contributions by Title and Abstract

About this book

Introduction

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.

Keywords

Monte Carlo method algorithms dynamics gauge theory mathematics mechanics physics quantum theory topology wave

Editors and affiliations

  • Cecile DeWitt-Morette
    • 1
  • Pierre Cartier
    • 2
  • Antoine Folacci
    • 3
  1. 1.The University of Texas at AustinAustinUSA
  2. 2.Ecole Normale SupérieureParisFrance
  3. 3.Université de CorseCorteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4899-0319-8
  • Copyright Information Springer-Verlag US 1997
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-0321-1
  • Online ISBN 978-1-4899-0319-8
  • Series Print ISSN 0258-1221
  • About this book