Classical and quantum dynamics: from classical paths to path integrals

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