Classical and Quantum Dynamics: From Classical Paths to Path Integrals

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Springer, Oct 8, 2015 - Science - 461 pages
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)
 

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Contents

1 Introduction
1
2 The Action Principles in Mechanics
3
3 The Action Principle in Classical Electrodynamics
17
4 Application of the Action Principles
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
Bibliography
457
Index
459
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About the author (2015)

Prof. Dr. Walter Dittrich had been head of the quantum electrodynamics group at the University of Tübingen. He started his work on gauge theories and QED in collaboration with Julian Schwinger. Walter Dittrich has worked for more than 20 years in cooperation with the Institute for Advanced Studies at Princeton and the National Accelerator Laboratory at Stanford (SLAC). He has over 30 years of teaching experience and is one of the key scientists in developing the theoretical framework of quantum electrodynamics.

Prof. Dr. Martin Reuter is head of the quantum Einstein gravity group at the Institute for High Energy Physics of the University Mainz. His research focuses on particle physics, quantum field theory and quantum Einstein gravity. He worked in close collaboration with the synchrotron facility DESY and the large hadron collider collaborations at CERN. He has more than 30 years of teaching experience in theoretical physics.

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