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E-grāmata: Functional Integration: Basics and Applications

  • Formāts: PDF+DRM
  • Sērija : NATO Science Series B: 361
  • Izdošanas datums: 11-Nov-2013
  • Izdevniecība: Kluwer Academic/Plenum Publishers
  • Valoda: eng
  • ISBN-13: 9781489903198
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  • Formāts: PDF+DRM
  • Sērija : NATO Science Series B: 361
  • Izdošanas datums: 11-Nov-2013
  • Izdevniecība: Kluwer Academic/Plenum Publishers
  • Valoda: eng
  • ISBN-13: 9781489903198
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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.

1. A Rigorous Mathematical Foundation of Functional Integration 1(50) P. Cartier C. DeWitt-Morette A. Wurm D. Collins
2. Physics on and near Caustics 51(16) C. DeWitt-Morette P. Cartier
3. Quantum Equivalence Principle 67(26) H. Kleinert
4. Variational Perturbation Theory for Path Integrals 93(4) H. Kleinert
5. Functional Integration and Wave Propagation 97(34) S. K. Foong
6. Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms 131(62) A. Sokal
7. Path Integral Simulation of Long-Time Dynamics in Quantum Dissipative Systems 193(20) N. Makri
8. Developpements Recents sur les Groupes de Tresses Applications a la Topologie et a lAlgebre 213(34) P. Cartier
9. An Introduction to Knot Theory and Functional Integrals 247(62) L. Kauffman
10. Locally Self-Avoiding Walks 309(18) D. Iagolnitzer J. Magnen
11. Gauge Theory without Ghosts 327(36) B. DeWitt C. Molina-Paris
12. Localization and Diagonalization: A Review of Functional Integral Techniques for Low-Dimensional Gauge Theories and Topological Field Theories 363(48) M. Blau G. Thompson Participants Contributions by Title and Abstract 411(14) A. Abdesselam I. G. Avramidi B. Bodmann S. Warzel V. Calian F. Castell B. DeWitt D. Endesfelder P. P. Fiziev R. Garattini D. M. Gitman C. Holm Y. Y. Lobanov A. Pelster H. Kleinert S. Pernice G. Piorot G. Samelsohn V. Schulte-Frohlinde E. Sim F. Spineanu M. Vlad B. M. Pimentel J. L. Tomazelli J. F. Willemsen K. Yildirim M. Znojil List of Participants 425(4) Index 429