Techniques and Applications of Path Integration

Partial table of contents: Probabilities and Probability Amplitudes for Paths. Correspondence Limit for the Path Integral (Heuristic). Vector Potentials and Another Proof of the Path Integral Formula. Doing the Integral: Free Particle and Quadratic Lagrangians. Brownian Motion and the Wiener Integral Kac's Proof. Perturbation Theory and Feynman Diagrams. SELECTED APPLICATIONS OF THE PATH INTEGRAL. Asymptotic Analysis. The Calculus of Variations. WKB Near Caustics. The Phase of the Semiclassical Amplitude. Scattering Theory. Geometrical Optics. The Polaron. Spin and Related Matters. Quantum Mechanics on Curved Spaces. Relativistic Propagators and Black Holes. Applications to Statistical Mechanics. Critical Droplets. Alias Instantons, and Metastability. Phase Space Path Integral. Omissions, Miscellany, and Prejudices. Indexes.