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Classical and Quantum Dynamics: From Classical Paths to Path Integrals de Walter Dittrich

Classical and Quantum Dynamics: From Classical Paths to Path Integrals

Autor Walter Dittrich, Martin Reuter
en Limba Engleză Paperback – 28 iul 2018
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.
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Specificații

ISBN-13: 9783319863696
ISBN-10: 331986369X
Pagini: 489
Ilustrații: XVI, 489 p. 18 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.7 kg
Ediția:Softcover reprint of the original 5th ed. 2017
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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) = Esinw0t; Schwinger-Fock Proper-Time Method.-  The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics.- Appendix.- Solutions.- Index.

Notă biografică

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. 

Textul de pe ultima copertă

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.

Caracteristici

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

Recenzii

“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)