Classical and Quantum Dynamics
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Classical and Quantum Dynamics: From Classical Paths to Path Integrals

Classical and Quantum Dynamics: From Classical Paths to Path Integrals

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About the Book

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 p-?-N physics and general relativity, where Riemann’s (Einstein’s) ideas on space and time and their philosophical implications are discussed.  

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.- 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.


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Product Details
  • ISBN-13: 9783030367855
  • Publisher: Springer Nature Switzerland AG
  • Binding: Hardback
  • Height: 235 mm
  • No of Pages: 563
  • Sub Title: From Classical Paths to Path Integrals
  • ISBN-10: 3030367851
  • Publisher Date: 07 Feb 2020
  • Edition: Revised edition
  • Language: English
  • Returnable: Y
  • Width: 155 mm


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