Classical and Quantum Dynamics: from Classical Paths to Path Integrals

Front Matter....Pages i-vii
Introduction....Pages 1-2
The Action Principles in Mechanics....Pages 3-14
Application of the Action Principles....Pages 15-33
Jacobi Fields, Conjugate Points....Pages 35-45
Canonical Transformations....Pages 47-60
The Hamilton-Jacobi Equation....Pages 61-73
Action-Angle Variables....Pages 75-96
The Adiabatic Invariance of the Action Variables....Pages 97-107
Time-Independent Canonical Perturbation Theory....Pages 109-115
Canonical Perturbation Theory with Several Degrees of Freedom....Pages 117-129
Canonical Adiabatic Theory....Pages 131-136
Removal of Resonances....Pages 137-145
Superconvergent Perturbation Theory, KAM Theorem (Introduction)....Pages 147-154
Poincaré Surface of Sections, Mappings....Pages 155-163
The KAM Theorem....Pages 165-171
Fundamental Principles of Quantum Mechanics....Pages 173-177
Examples for Calculating Path Integrals....Pages 179-198
Direct Evaluation of Path Integrals....Pages 199-208
Linear Oscillator with Time-Dependent Frequency....Pages 209-223
Propagators for Particles in an External Magnetic Field....Pages 225-229
Simple Applications of Propagator Functions....Pages 231-246
The WKB Approximation....Pages 247-256
Partition Function for the Harmonic Oscillator....Pages 257-262
Introduction to Homotopy Theory....Pages 263-267
Classical Chern-Simons Mechanics....Pages 269-279
Semiclassical Quantization....Pages 281-286
The “Maslov Anomaly” for the Harmonic Oscillator....Pages 287-294
Maslov Anomaly and the Morse Index Theorem....Pages 295-300
Berry’s Phase....Pages 301-309
Classical Analogues to Berry’s Phase....Pages 311-322
Berry Phase and Parametric Harmonic Oscillator....Pages 323-335
Back Matter....Pages 337-341