Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)

By William White

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.- Poincar? 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. This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 3540519920
• ISBN13: 9783540519928
• Release Date: January 1992
• Publisher: Springer
• Length: 349 Pages