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Classical and quantum dynamicsfrom c...

Dittrich, Walter.

Classical and quantum dynamicsfrom classical paths to path integrals /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Classical and quantum dynamicsby Walter Dittrich, Martin Reuter.
Reminder of title:	from classical paths to path integrals /
Author:	Dittrich, Walter.
other author:	Reuter, Martin.
Published:	Cham :Springer International Publishing :2016.
Description:	xii, 461 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Quantum theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-21677-5
ISBN:	9783319216775$q(electronic bk.)

Classical and quantum dynamicsfrom classical paths to path integrals /
Dittrich, Walter.

Classical and quantum dynamicsfrom classical paths to path integrals /[electronic resource] :by Walter Dittrich, Martin Reuter. - 4th ed. - Cham :Springer International Publishing :2016. - xii, 461 p. :ill., digital ;24 cm. - Graduate texts in physics,1868-4513. - Graduate texts in physics..

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 -- Poincare 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 Analogues to Berry's Phase -- Berry Phase and Parametric Harmonic Oscillator -- Topological Phases in Planar Electrodynamics -- Appendix -- Solutions -- Index.

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)

ISBN: 9783319216775$q(electronic bk.)

Standard No.: 10.1007/978-3-319-21677-5doiSubjects--Topical Terms:

199020
Quantum theory.

LC Class. No.: QC174.12

Dewey Class. No.: 530.12

Classical and quantum dynamicsfrom classical paths to path integrals /
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505 0 $a 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 -- Poincare 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 Analogues to Berry's Phase -- Berry Phase and Parametric Harmonic Oscillator -- Topological Phases in Planar Electrodynamics -- Appendix -- Solutions -- Index.
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