Classical and Quantum Dynamics: From Classical Paths to Path Integrals / Edition 3

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Overview

Physics students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here a detailed treatment many worked examples. This new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.

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Editorial Reviews

From the Publisher
From the reviews of the third edition:

"This book is a brilliant exposition of dynamical systems covering the essential aspects and written in an elegant manner. The book is written in modern language of mathematics and will ideally cater to the requirements of graduate and first year Ph.D. students...a wonderful introduction to any student who wants to do research in any branch of theoretical Physics."

—Indian Journal of Physics

"The point which makes this book really unique is the abundance of detailed well-chosen examples illustrating the action principle, the canonical transformations, the perturbation theory, and the removal of resonances...Numerous explicit examples of direct evaluations of path integrals make this approach particularly clear and attractive. This book will be of interest to both graduate and post-graduate advanced physics students and is warmly recommended in view of its originality and readability."

—Physicalia

"The search of possible connections between classical dynamics and quantum mechanics is an old exciting problem. … The present book highlights the principle of stationary action as common starting point of both theories. … This third edition … is supplemented with chapters on the action principle in classical electrodynamics (an excellent example of working scheme), on the functional derivative approach and on computing traces in the context of WKB propagator. Extensive additions and detailed treatments are also included in the text." (Mircea Crâsmareanu, Zentralblatt MATH, Vol. 990 (15), 2002)

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Product Details

  • ISBN-13: 9783540420668
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 8/9/2001
  • Series: Advanced Texts in Physics Series
  • Edition description: Softcover reprint of the original 3rd ed. 2001
  • Edition number: 3
  • Pages: 385
  • Product dimensions: 0.82 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

1. The Action Principles in Mechanics.- 2. The Action Principle in Classical Electrodynamics.- 3. Application of the Action Principles.- 4. Jacobi Fields, Conjugate Points.- 5. Canonical Transformations.- 6. The Hamilton—Jacobi Equation.- 7. Action-Angle Variables.- 8. The Adiabatic Invariance of the Action Variables.- 9. Time-Independent Canonical Perturbation Theory.- 10. Canonical Perturbation Theory with Several Degrees of Freedom.- 11. Canonical Adiabatic Theory.- 12. Removal of Resonances.- 13. Superconvergent Perturbation Theory, KAM Theorem (Introduction).- 14. Poincaré Surface of Sections, Mappings.- 15. The KAM Theorem.- 16. Fundamental Principles of Quantum Mechanics.- 17. Functional Derivative Approach.- 18. Examples for Calculating Path Integrals.- 19. Direct Evaluation of Path Integrals.- 20. Linear Oscillator with Time-Dependent Frequency.- 21. Propagators for Particles in an External Magnetic Field.- 22. Simple Applications of Propagator Functions.- 23. The WKB Approximation.- 24. Computing the trace.- 25. Partition Function for the Harmonic Oscillator.- 26. Introduction to Homotopy Theory.- 27. Classical Chern—Simons Mechanics.- 28. Semiclassical Quantization.- 29. The “Maslov Anomaly” for the Harmonic Oscillator.- 30. Maslov Anomaly and the Morse Index Theorem.- 31. Berry’s Phase.- 32. Classical Analogues to Berry’s Phase.- 33. Berry Phase and Parametric Harmonie Oscillator.- 34. Topological Phases in Planar Electrodynamics.- References.

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