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  • © 2016

Classical and Quantum Dynamics

From Classical Paths to Path Integrals

  • Highlights the principle of stationary action as common starting point of classical and quantum mechanics
  • Contains numerous detailed examples
  • Includes new chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction

Part of the book series: Graduate Texts in Physics (GTP)

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Table of contents (38 chapters)

  1. Front Matter

    Pages i-xiv
  2. Introduction

    • Walter Dittrich, Martin Reuter
    Pages 1-2
  3. The Action Principles in Mechanics

    • Walter Dittrich, Martin Reuter
    Pages 3-16
  4. The Action Principle in Classical Electrodynamics

    • Walter Dittrich, Martin Reuter
    Pages 17-22
  5. Application of the Action Principles

    • Walter Dittrich, Martin Reuter
    Pages 23-44
  6. Jacobi Fields, Conjugate Points

    • Walter Dittrich, Martin Reuter
    Pages 45-57
  7. Canonical Transformations

    • Walter Dittrich, Martin Reuter
    Pages 59-74
  8. The Hamilton–Jacobi Equation

    • Walter Dittrich, Martin Reuter
    Pages 75-92
  9. Action-Angle Variables

    • Walter Dittrich, Martin Reuter
    Pages 93-117
  10. The Adiabatic Invariance of the Action Variables

    • Walter Dittrich, Martin Reuter
    Pages 119-131
  11. Time-Independent Canonical Perturbation Theory

    • Walter Dittrich, Martin Reuter
    Pages 133-140
  12. Canonical Perturbation Theory with Several Degrees of Freedom

    • Walter Dittrich, Martin Reuter
    Pages 141-156
  13. Canonical Adiabatic Theory

    • Walter Dittrich, Martin Reuter
    Pages 157-163
  14. Removal of Resonances

    • Walter Dittrich, Martin Reuter
    Pages 165-174
  15. Superconvergent Perturbation Theory, KAM Theorem (Introduction)

    • Walter Dittrich, Martin Reuter
    Pages 175-183
  16. Poincaré Surface of Sections, Mappings

    • Walter Dittrich, Martin Reuter
    Pages 185-195
  17. The KAM Theorem

    • Walter Dittrich, Martin Reuter
    Pages 197-204
  18. Fundamental Principles of Quantum Mechanics

    • Walter Dittrich, Martin Reuter
    Pages 205-209
  19. Functional Derivative Approach

    • Walter Dittrich, Martin Reuter
    Pages 211-222
  20. Examples for Calculating Path Integrals

    • Walter Dittrich, Martin Reuter
    Pages 223-245

About this book

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)

Reviews

“This is the fourth edition of a highly successful pedagogical book that combines classical and quantum dynamics, often viewed as disjoint subjects. … Its elementary exposition makes the book accessible to graduate students.” (Gert Roepstorff, zbMATH 1330.81001, 2016)

Authors and Affiliations

  • Institute of Theoretical Physics, University of Tübingen, Tübingen, Germany

    Walter Dittrich

  • Institute of Physics, University of Mainz, Mainz, Germany

    Martin Reuter

About the authors

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. 

Bibliographic Information

Buy it now

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access