Classical and quantum dynamics : from classical paths to path integrals / Walter Dittrich, Martin Reuter

By:

Dittrich, Walter, 1935- [VerfasserIn]

Contributor(s):

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer eBook CollectionPublisher: Cham : Imprint: Springer, [2020]Copyright date: © 2020Edition: 6th editionDescription: 1 Online-Ressource (X, 563 Seiten) : IllustrationenISBN:

9783030367862

Subject(s):

Additional physical formats: 9783030367855 | 9783030367879 | 9783030367886 | Erscheint auch als: 9783030367855 Druck-Ausgabe | Erscheint auch als: 9783030367879 Druck-Ausgabe | Erscheint auch als: 9783030367886 Druck-AusgabeDOI: DOI: 10.1007/978-3-030-36786-2Online resources:

Summary: 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.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. .PPN: PPN: 1691523844Package identifier: Produktsigel: ZDB-2-PHA | ZDB-2-SEB | ZDB-2-SXP

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