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Index
Cover Frontmatter 1. Introduction 2. The Action Principles in Mechanics 3. The Action Principle in Classical Electrodynamics 4. Application of the Action Principles 5. Jacobi Fields, Conjugate Points 6. Canonical Transformations 7. The Hamilton–Jacobi Equation 8. Action-Angle Variables 9. The Adiabatic Invariance of the Action Variables 10. Time-Independent Canonical Perturbation Theory 11. Canonical Perturbation Theory with Several Degrees of Freedom 12. Canonical Adiabatic Theory 13. Removal of Resonances 14. Superconvergent Perturbation Theory, KAM Theorem (Introduction) 15. Poincaré Surface of Sections, Mappings 16. The KAM Theorem 17. Fundamental Principles of Quantum Mechanics 18. Functional Derivative Approach 19. Examples for Calculating Path Integrals 20. Direct Evaluation of Path Integrals 21. Linear Oscillator with Time-Dependent Frequency 22. Propagators for Particles in an External Magnetic Field 23. Simple Applications of Propagator Functions 24. The WKB Approximation 25. Computing the Trace 26. Partition Function for the Harmonic Oscillator 27. Introduction to Homotopy Theory 28. Classical Chern–Simons Mechanics 29. Semiclassical Quantization 30. The “Maslov Anomaly” for the Harmonic Oscillator 31. Maslov Anomaly and the Morse Index Theorem 32. Berry’s Phase 33. Classical Analogues to Berry’s Phase 34. Berry Phase and Parametric Harmonic Oscillator 35. Topological Phases in Planar Electrodynamics 36. Path Integral Formulation of Quantum Electrodynamics 37. Particle in Harmonic E-Field E(t) = Esinω 0 t; Schwinger–Fock Proper-Time Method Backmatter
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