Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)

Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, together with many worked examples throughout the text. 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. Front Matter....Pages I-X Introduction....Pages 1-2 The Action Principles in Mechanics....Pages 3-14 The Action Principle in Classical Electrodynamics....Pages 15-19 Application of the Action Principles....Pages 21-40 Jacobi Fields, Conjugate Points....Pages 41-52 Canonical Transformations....Pages 53-66 The Hamilton—Jacobi Equation....Pages 67-82 Action-Angle Variables....Pages 83-104 The Adiabatic Invariance of the Action Variables....Pages 105-115 Time-Independent Canonical Perturbation Theory....Pages 117-123 Canonical Perturbation Theory with Several Degrees of Freedom....Pages 125-138 Canonical Adiabatic Theory....Pages 139-144 Removal of Resonances....Pages 145-153 Superconvergent Perturbation Theory, KAM Theorem (Introduction)....Pages 155-162 Poincaré Surface of Sections, Mappings....Pages 163-172 The KAM Theorem....Pages 173-179 Fundamental Principles of Quantum Mechanics....Pages 181-185 Functional Derivative Approach....Pages 187-196 Examples for Calculating Path Integrals....Pages 197-216 Direct Evaluation of Path Integrals....Pages 217-226 Linear Oscillator with Time-Dependent Frequency....Pages 227-241 Propagators for Particles in an External Magnetic Field....Pages 243-247 Simple Applications of Propagator Functions....Pages 249-264 The WKB Approximation....Pages 265-274 Computing the Trace....Pages 275-279 Partition Function for the Harmonic Oscillator....Pages 281-286 Introduction to Homotopy Theory....Pages 287-291 Classical Chern—Simons Mechanics....Pages 293-304 Semiclassical Quantization....Pages 305-310 The “Maslov Anomaly” for the Harmonic Oscillator....Pages 311-318 Maslov Anomaly and the Morse Index Theorem....Pages 319-324 Berry’s Phase....Pages 325-340 Classical Analogues to Berry’s Phase....Pages 341-356 Berry Phase and Parametric Harmonic Oscillator....Pages 357-369 Topological Phases in Planar Electrodynamics....Pages 371-379 Back Matter....Pages 381-385 Machine generated contents note: Introduction 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. Poincare 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 Chem-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 Harmonic Oscillator 34. Topological Phases in Planar Electrodynamics References Index. Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, together with many worked examples throughout the text. This second edition has been enlarged by a new chapter on topological phases in planar electrodynamics and a discussion of the Aharonov-Bohm effect. 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. Book by Dittrich, Walter, Reuter, Martin