Classical and Quantum Dynamics Book

	Introduction	1
1	The Action Principles in Mechanics	3
2	The Action Principle in Classical Electrodynamics	15
3	Application of the Action Principles	21
4	Jacobi Fields, Conjugate Points	41
5	Canonical Transformations	53
6	The Hamilton-Jacobi Equation	67
7	Action-Angle Variables	83
8	The Adiabatic Invariance of the Action Variables	105
9	Time-Independent Canonical Perturbation Theory	117
10	Canonical Perturbation Theory with Several Degrees of Freedom	125
11	Canonical Adiabatic Theory	139
12	Removal of Resonances	145
13	Superconvergent Perturbation Theory, KAM Theorem (Introduction)	155
14	Poincare Surface of Sections, Mappings	163
15	The KAM Theorem	173
16	Fundamental Principles of Quantum Mechanics	181
17	Functional Derivative Approach	187
18	Examples for Calculating Path Integrals	197
19	Direct Evaluation of Path Integrals	217
20	Linear Oscillator with Time-Dependent Frequency	227
21	Propagators for Particles in an External Magnetic Field	243
22	Simple Applications of Propagator Functions	249
23	The WKB Approximation	265
24	Computing the trace	275
25	Partition Function for the Harmonic Oscillator	281
26	Introduction to Homotopy Theory	287
27	Classical Chern-Simons Mechanics	293
28	Semiclassical Quantization	305
29	The "Maslov Anomaly" for the Harmonic Oscillator	311
30	Maslov Anomaly and the Morse Index Theorem	319
31	Berry's Phase	325
32	Classical Analogues to Berry's Phase	341
33	Berry Phase and Parametric Harmonic Oscillator	357
34	Topological Phases in Planar Electrodynamics	371
	References	381
	Index	383