Classical and quantum dynamics: From classical paths to path integrals

Preface to the Sixth Edition......Page 5
Preface to the First Edition......Page 7
Contents......Page 8
1 Introduction......Page 10
2 The Action Principles in Mechanics......Page 12
3 The Action Principle in Classical Electrodynamics......Page 26
4 Application of the Action Principles......Page 32
5 Jacobi Fields, Conjugate Points......Page 54
6 Canonical Transformations......Page 67
7 The Hamilton–Jacobi Equation......Page 83
8 Action-Angle Variables......Page 101
9 The Adiabatic Invariance of the Action Variables......Page 126
10 Time-Independent Canonical Perturbation Theory......Page 139
11 Canonical Perturbation Theory with Several Degrees of Freedom......Page 147
12 Canonical Adiabatic Theory......Page 163
13 Removal of Resonances......Page 170
14 Superconvergent Perturbation Theory, KAM Theorem (Introduction)......Page 180
15 Poincaré Surface of Sections, Mappings......Page 189
16 The KAM Theorem......Page 200
17 Fundamental Principles of Quantum Mechanics......Page 208
18 Functional Derivative Approach......Page 213
19 Examples for Calculating Path Integrals......Page 225
20 Direct Evaluation of Path Integrals......Page 248
21 Linear Oscillator with Time-Dependent Frequency......Page 260
22 Propagators for Particles in an External Magnetic Field......Page 276
23 Simple Applications of Propagator Functions......Page 282
24 The WKB Approximation......Page 300
25 Computing the Trace......Page 312
26 Partition Function for the Harmonic Oscillator......Page 318
27 Introduction to Homotopy Theory......Page 325
28 Classical Chern–Simons Mechanics......Page 331
29 Semiclassical Quantization......Page 344
30 The ``Maslov Anomaly'' for the Harmonic Oscillator......Page 351
31 Maslov Anomaly and the Morse Index Theorem......Page 360
32 Berry's Phase......Page 367
33 Classical Geometric Phases: Foucault and Euler......Page 385
34 Berry Phase and Parametric Harmonic Oscillator......Page 404
35 Topological Phases in Planar Electrodynamics......Page 419
36 Path Integral Formulation of Quantum Electrodynamics......Page 429
37 Particle in Harmonic E-Field E(t)= E sinω0 t; Schwinger–Fock Proper-Time Method......Page 438
38 The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics......Page 451
39 Green's Function of a Spin- eepic12 Particle in a Constant External Magnetic Field......Page 476
40 One-Loop Effective Lagrangian in QED......Page 489
 Riemann's Unit Sphere S2......Page 497
 Riemann's Unit Sphere Sn......Page 499
 Derivation of Riemann's Main Formula for ds2......Page 501
 Calculation of Riemann's Curvature Tensor, Ricci Scalar, etc.; Maximally Symmetric Metric......Page 503
 Realization of Chiral Symmetry in a Curved Isospin Space......Page 513
 Schwinger's Source Treatment of the Low-Energy π-N System......Page 514
 How the Pion Gets Its Mass......Page 522
42 The Non-Abelian Vector Gauge Particle ρ......Page 529
43 Riemann's Result and Consequences for Physics and Philosophy......Page 543
Bibliography......Page 546
Index......Page 549