rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Classical and Quantum Dynamics
    sub title: From Classical Paths to Path Integrals
  name:
    name part: Dittrich, Walter.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Reuter, Martin.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    edition: 5th ed. 2017.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 489 p. 18 illus. online resource.
  abstract: 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.
  table of 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.
  note: by Walter Dittrich, Martin Reuter.
  subject:
    topic: Physics
  subject:
    topic: Mathematical physics
  subject:
    topic: Quantum physics
  subject:
    topic: Nuclear physics
  subject:
    topic: Physics
  subject:
    topic: Quantum Physics
  subject:
    topic: Classical and Continuum Physics
  subject:
    topic: Mathematical Applications in the Physical Sciences
  subject:
    topic: Particle and Nuclear Physics
  classification: QC173.96-174.52
  classification: 530.12
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319582986
  identifier: http://dx.doi.org/10.1007/978-3-319-58298-6
  record info:
    record creation date: 170513
    record change date: 20170513150938.0
    record identifier: 978-3-319-58298-6