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ISBN 10: 0486445283
ISBN 13: 978-0486445281
Author: L. S. Schulman
Introduction and Defining the Path Integral
Appendix: The Trotter Product Formula
Probabilities and Probability Amplitudes for Paths
Correspondence Limit for the Path Integral (Heuristic)
Appendix: Useful Integrals
Vector Potentials and Another Proof of the Path Integral Formula
The Ito Integral and Gauge Transformations
Doing the Integral: Free Particle and Quadratic Lagrangians
Appendix: Exactness of the Sum over Classical Paths
Properties of Green's Functions; the Feynman-Kac Formula
Functional Derivatives and Commutation Relations
Brownian Motion and the Wiener Integral; Kac's Proof
Perturbation Theory and Feynman Diagrams
Asymptotic Analysis
The Calculus of Variations
The WKB Approximation and its Application to the Anharmonic Oscillator
Detailed Presentation of the WKB Approximation
WKB Near Caustics
Caustics and Uniform Asymptotic Approximations
The Phase of the Semiclassical Amplitude
The Semiclassical Propagator as a Function of Energy
Scattering Theory
Geometrical Optics
The Polaron
Spin and Related Matters
22.1 The Direct Method – Product Integrals or Time Ordered Products
22.2 Continuous Models for Spin
Path Integrals for Multiply Connected Spaces
23.1 Particle Constrained to a Circle
23.2 Rudiments of Homotopy Theory
23.3 Homotopy Applied to the Path Integral
23.4 Extensions of Symmetric Operators
Quantum Mechanics on Curved Spaces
Relativistic Propagators and Black Holes
Applications to Statistical Mechanics
Coherent State Representation
Systems with Random Impurities
Critical Droplets, Alias Instantons, and Metastability
Appendix: Small Oscillations about the Instanton
Renormalization and Scaling for Critical Phenomena
Phase Space Path Integral
Omissions, Miscellany, and Prejudices
32.1 Field Theory
32.2 Uncompleting the Square
32.3 Rubber: Path Integral Formulation of a Polymer as a Random Walk
32.4 Hard Sphere Gas Second Virial Coefficient
32.5 Adding Paths by Computer
32.6 A Perturbation Expansion Using the Path Integral
32.7 Solvable Path Integral with the Potential ax² + b/x²
32.8 Superfluidity
32.9 Fermions
32.10 Books and Review Papers on Path Integrals
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Tags: Schulman, Techniques, Applications, Integration
