Classical and Quantum Dynamics: From Classical Paths to Path Integrals

✍ Scribed by Walter Dittrich, Martin Reuter

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 458
• Series: Graduate Texts in Physics
• Edition: 4ed.
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xii
Introduction....Pages 1-2
The Action Principles in Mechanics....Pages 3-16
The Action Principle in Classical Electrodynamics....Pages 17-22
Application of the Action Principles....Pages 23-44
Jacobi Fields, Conjugate Points....Pages 45-57
Canonical Transformations....Pages 59-74
The Hamilton–Jacobi Equation....Pages 75-92
Action-Angle Variables....Pages 93-117
The Adiabatic Invariance of the Action Variables....Pages 119-131
Time-Independent Canonical Perturbation Theory....Pages 133-140
Canonical Perturbation Theory with Several Degrees of Freedom....Pages 141-156
Canonical Adiabatic Theory....Pages 157-163
Removal of Resonances....Pages 165-174
Superconvergent Perturbation Theory, KAM Theorem (Introduction)....Pages 175-183
Poincaré Surface of Sections, Mappings....Pages 185-195
The KAM Theorem....Pages 197-204
Fundamental Principles of Quantum Mechanics....Pages 205-209
Functional Derivative Approach....Pages 211-222
Examples for Calculating Path Integrals....Pages 223-245
Direct Evaluation of Path Integrals....Pages 247-258
Linear Oscillator with Time-Dependent Frequency....Pages 259-274
Propagators for Particles in an External Magnetic Field....Pages 275-280
Simple Applications of Propagator Functions....Pages 281-298
The WKB Approximation....Pages 299-310
Computing the Trace....Pages 311-316
Partition Function for the Harmonic Oscillator....Pages 317-323
Introduction to Homotopy Theory....Pages 325-330
Classical Chern–Simons Mechanics....Pages 331-343
Semiclassical Quantization....Pages 345-351
The “Maslov Anomaly” for the Harmonic Oscillator....Pages 353-361
Maslov Anomaly and the Morse Index Theorem....Pages 363-369
Berry’s Phase....Pages 371-388
Classical Analogues to Berry’s Phase....Pages 389-406
Berry Phase and Parametric Harmonic Oscillator....Pages 407-421
Topological Phases in Planar Electrodynamics....Pages 423-432
Path Integral Formulation of Quantum Electrodynamics....Pages 433-441
Back Matter....Pages 443-455
....Pages 457-461

✦ Subjects

Quantum theory;Physics;Mathematical physics;Field theory (Physics);Nuclear physics