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  • © 2017

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
  • Perfect companion for courses on path integrals, on advanced mechanics or quantum mechanics and semiclassical methods
  • New edition showcases updates for all chapters and a new chapter with a clear and explicit account of Lie-Brackets and pseudocanonical transformations
  • Includes supplementary material: sn.pub/extras
  • Includes supplementary material: sn.pub/extras

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Table of contents (38 chapters)

  1. Front Matter

    Pages i-xvi
  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 wish 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 fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.

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 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
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