## Classical and Quantum Dynamics: From Classical Paths to Path IntegralsGraduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction. "This book is a brilliant exposition of dynamical systems covering the essential aspects and written in an elegant manner. The book is written in modern language of mathematics and will ideally cater to the requirements of graduate and first year Ph.D. students...a wonderful introduction to any student who wants to do research in any branch of theoretical Physics." (Indian Journal of Physics) |

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### Contents

1 | |

3 | |

17 | |

23 | |

5 Jacobi Fields Conjugate Points | 45 |

6 Canonical Transformations | 59 |

7 The HamiltonJacobi Equation | 75 |

8 ActionAngle Variables | 93 |

22 Propagators for Particles in an External Magnetic Field | 275 |

23 Simple Applications of Propagator Functions | 281 |

24 The WKB Approximation | 299 |

25 Computing the Trace | 311 |

26 Partition Function for the Harmonic Oscillator | 317 |

27 Introduction to Homotopy Theory | 325 |

28 Classical ChernSimons Mechanics | 331 |

29 Semiclassical Quantization | 344 |

9 The Adiabatic Invariance of the Action Variables | 118 |

10 TimeIndependent Canonical Perturbation Theory | 133 |

11 Canonical Perturbation Theory with Several Degrees of Freedom | 141 |

12 Canonical Adiabatic Theory | 157 |

13 Removal of Resonances | 164 |

14 Superconvergent Perturbation Theory KAM Theorem Introduction | 175 |

15 Poincaré Surface of Sections Mappings | 185 |

16 The KAM Theorem | 196 |

17 Fundamental Principles of Quantum Mechanics | 205 |

18 Functional Derivative Approach | 211 |

19 Examples for Calculating Path Integrals | 223 |

20 Direct Evaluation of Path Integrals | 246 |

21 Linear Oscillator with TimeDependent Frequency | 259 |

30 The Maslov Anomaly for the Harmonic Oscillator | 353 |

31 Maslov Anomaly and the Morse Index Theorem | 362 |

32 Berrys Phase | 371 |

33 Classical Analogues to Berrys Phase | 389 |

34 Berry Phase and Parametric Harmonic Oscillator | 407 |

35 Topological Phases in Planar Electrodynamics | 422 |

36 Path Integral Formulation of Quantum Electrodynamics | 433 |

37 Particle in Harmonic EField Et E sinω0 t SchwingerFock ProperTime Method | 443 |

Classical and Quantum Dynamics From Classical Paths to Path Integrals | 456 |

457 | |

459 | |

### Other editions - View all

Classical and Quantum Dynamics: From Classical Paths to Path Integrals Walter Dittrich,Martin Reuter No preview available - 2015 |

Classical and Quantum Dynamics: From Classical Paths to Path Integrals Walter Dittrich,Martin Reuter No preview available - 2015 |

### Common terms and phrases

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