Classical and quantum dynamics From classical paths to path integrals 6th Edition Dittrich W 303036786X 9783030367862

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Product details:

• ISBN-10: 303036786X 
• ISBN-13: 9783030367862
• Author: Dittrich W

Graduate students seeking to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book 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 just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals.   The sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger’s source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed.

Table of contents:

1. Introduction
2. The Action Principles in Mechanics
3. The Action Principle in Classical Electrodynamics
4. Application of the Action Principles
5. Jacobi Fields, Conjugate Points
6. Canonical Transformations
7. The Hamilton–Jacobi Equation
8. Action-Angle Variables
9. The Adiabatic Invariance of the Action Variables
10. Time-Independent Canonical Perturbation Theory
11. Canonical Perturbation Theory with Several Degrees of Freedom
12. Canonical Adiabatic Theory
13. Removal of Resonances
14. Superconvergent Perturbation Theory, KAM Theorem (Introduction)
15. Poincaré Surface of Sections, Mappings
16. The KAM Theorem
17. Fundamental Principles of Quantum Mechanics
18. Functional Derivative Approach
19. Examples for Calculating Path Integrals
20. Direct Evaluation of Path Integrals
21. Linear Oscillator with Time-Dependent Frequency
22. Propagators for Particles in an External Magnetic Field
23. Simple Applications of Propagator Functions
24. The WKB Approximation
25. Computing the Trace
26. Partition Function for the Harmonic Oscillator
27. Introduction to Homotopy Theory
28. Classical Chern–Simons Mechanics
29. Semiclassical Quantization
30. The “Maslov Anomaly” for the Harmonic Oscillator
31. Maslov Anomaly and the Morse Index Theorem
32. Berry’s Phase
33. Classical Geometric Phases: Foucault and Euler
34. Berry Phase and Parametric Harmonic Oscillator
35. Topological Phases in Planar Electrodynamics
36. Path Integral Formulation of Quantum Electrodynamics
37. Particle in Harmonic E-Field ; Schwinger–Fock Proper-Time Method
38. The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics
39. Green’s Function of a Spin- Particle in a Constant External Magnetic Field
40. One-Loop Effective Lagrangian in QED
41. On Riemann’s Ideas on Space and Schwinger’s Treatment of Low-Energy Pion-Nucleon Physics
42. The Non-Abelian Vector Gauge Particle ρ
43. Riemann’s Result and Consequences for Physics and Philosophy

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