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CLASSICAL AND QUANTUM DYNAMICS : from classical paths to path integrals.
Author
Dittrich, Walter
[Browse]
Format
Book
Language
English
Published/Created
[S.l.] : SPRINGER, 2017.
Description
xvi, 489 pages ; 24 cm
Availability
Available Online
Springer Nature - Springer Physics and Astronomy eBooks 2017 English International
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QC174.12 .D58 2017
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Details
Subject(s)
Quantum theory
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Mathematical physics
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Field theory (Physics)
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Summary note
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.
Bibliographic references
Includes bibliographical references and index.
Contents
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.
Show 36 more Contents items
ISBN
3319582976 ((hardcover))
9783319582979 ((hardcover))
OCLC
983276586
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Other versions
Classical and Quantum Dynamics [electronic resource] : From Classical Paths to Path Integrals / by Walter Dittrich, Martin Reuter.
id
99125381679206421