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