Classical and Quantum Dynamics : From Classical Paths to Path Integrals / by Walter Dittrich, Martin Reuter.

Format:

Book

Author/Creator:

Dittrich, Walter, author.

Reuter, Martin, 1958- author.

Contributor:

SpringerLink (Online service)

Series:

Physics and Astronomy (Springer-11651)

Language:

English

Subjects (All):

Quantum theory.

Field theory (Physics).

Mathematical physics.

Nuclear physics.

Statistical physics.

Quantum Physics.

Classical and Continuum Physics.

Mathematical Applications in the Physical Sciences.

Particle and Nuclear Physics.

Statistical Physics and Dynamical Systems.

Local Subjects:

Quantum Physics.

Classical and Continuum Physics.

Mathematical Applications in the Physical Sciences.

Particle and Nuclear Physics.

Statistical Physics and Dynamical Systems.

Physical Description:

1 online resource (X, 563 pages) : 307 illustrations

Edition:

Sixth edition 2020.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2020.

System Details:

text file PDF

Summary:

Graduate students seeking 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 sixth edition has been enlarged to include the Heisenberg-Euler Lagrangian, Schwinger's source theory treatment of the low-energy π-ρ-N physics and general relativity, where Riemann's (Einstein's) ideas on space and time and their philosophical implications are discussed. .

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

Green's Function of a Spin-1/2 Particle in a Constant External Magnetic Field

One-Loop Effective Lagrangian in QED

On Riemann's Ideas on Space and Schwinger's Treatment of Low-Energy Pion-Nucleon Physics

The Non-Abelian Vector Gauge Particle p

Riemann's Result and Consequences for Physics and Philosophy.

Other Format:

Printed edition:

ISBN:

978-3-030-36786-2

9783030367862

Access Restriction:

Restricted for use by site license.