Classical and Quantum Dynamics: From Classical Paths to Path Integrals 4th Edition Walter 3319216775 9783319216775

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Product details:

• ISBN-10 ‏ : ‎ 3319216775
• ISBN-13 ‏ : ‎ 9783319216775
• Author: Walter Dittrich

Graduate 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)

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 Analogues to Berry’s Phase
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 E(t) = Esinω 0 t; Schwinger–Fock Prope

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