Classical and Quantum Dynamics
From Classical Paths to Path Integrals
5th Edition
Published on 11. May 2017
XVI, 489 pages
978-3-319-58298-6 (ISBN)
Description
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.
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.
More details
Series
Edition
5th ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
XVI, 489 p. 18 illus.
ISBN-13
978-3-319-58298-6 (9783319582986)
DOI
10.1007/978-3-319-58298-6
Schweitzer Classification
Other editions
New editions
Walter Dittrich | Martin Reuter
Classical and Quantum Dynamics
From Classical Paths to Path Integrals
E-Book
02/2020
6th Edition
Springer
€69.54
Available for download
Additional editions
Walter Dittrich | Martin Reuter
Classical and Quantum Dynamics
From Classical Paths to Path Integrals
Book
05/2017
5th Edition
Springer
€74.89
Article exhausted; check for reprint
Previous edition
Walter Dittrich | Martin Reuter
Classical and Quantum Dynamics
From Classical Paths to Path Integrals
E-Book
10/2015
4th Edition
Springer
€64.19
Available for download
Persons
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.
Content
Introduction.- The Action Principles in Mechanics.- The Action Principle in Classical Electrodynamics.- Application of the Action Principles.- Jacobi Fields, Conjugate Points.-Canonical Transformations.- The Hamilton-Jacobi Equation.- Action-Angle Variables.- The Adiabatic Invariance of the Action Variables.- Time-Independent Canonical Perturbation Theory .- Canonical Perturbation Theory with Several Degrees of Freedom.- Canonical Adiabatic Theory.- Removal of Resonances.- Superconvergent Perturbation Theory, KAM Theorem.- Poincaré Surface of Sections, Mappings.- The KAM Theorem.- Fundamental Principles of Quantum Mechanics.- Functional Derivative Approach.- Examples for Calculating Path Integrals.- Direct Evaluation of Path Integrals.- Linear Oscillator with Time-Dependent Frequency.- Propagators for Particles in an External Magnetic Field.- Simple Applications of Propagator Functions.- The WKB Approximation.- Computing the trace.- Partition Function for the Harmonic Oscillator.- Introduction to Homotopy Theory.- Classical Chern-Simons Mechanics.- Semiclassical Quantization.- The "Maslov Anomaly" for the Harmonic Oscillator.-Maslov Anomaly and the Morse Index Theorem.- Berry's Phase.- Classical Geometric Phases: Foucault and Euler.- Berry Phase and Parametric Harmonic Oscillator.- Topological Phases in Planar Electrodynamics.- Path Integral Formulation of Quantum Electrodynamics.- Particle in Harmonic E-Field E(t) = Esin
w0
t; Schwinger-Fock Proper-Time Method.- The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics.- Appendix.- Solutions.- Index.
