Techniques and Applications of Path Integration

L. S. Schulman

Publisher:

Dover Publications

Publication Date:

2006

Number of Pages:

416

Format:

Paperback

Price:

21.95

ISBN:

0486445283

Category:

Monograph

MAA Review
Table of Contents

We do not plan to review this book.

Part I	Introduction
	1	Introduction and Defining the Path Integral
		Appendix: The Trotter Product Formula
	2	Probabilities and Probability Amplitudes for Paths
	3	Correspondence Limit for the Path Integral (Heuristic)
		Appendix: Useful Integrals
	4	Vector Potentials and Another Proof of the Path Integral Formula
	5	The Ito Integral and Gauge Transformations
	6	Doing the Integral: Free Particle and Quadratic Lagrangians
		Appendix: Exactness of the Sum over Classical Paths
	7	Properties of Green's Functions; the Feynman-Kac Formula
	8	Functional Derivatives and Commutation Relations
	9	Brownian Motion and the Wiener Integral; Kac's Proof
	10	Perturbation Theory and Feynman Diagrams
Part II	Selected Applications of the Path Integral
	11	Asymptotic Analysis
	12	The Calculus of Variations
	13	The WKB Approximation and its Application to the Anharmonic Oscillator
	14	Detailed Presentation of the WKB Approximation
	15	WKB Near Caustics
	16	Caustics and Uniform Asymptotic Approximations
	17	The Phase of the Semiclassical Amplitude
	18	The Semiclassical Propagator as a Function of Energy
	19	Scattering Theory
	20	Geometrical Optics
	21	The Polaron
	22	Spin and Related Matters
		22.1	The Direct Method-Product Integrals or Time Ordered Products
		22.2	Continuous Models for Spin
	23	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
	24	Quantum Mechanics on Curved Spaces
	25	Relativistic Propagators and Black Holes
	26	Applications to Statistical Mechanics
	27	Coherent State Representation
	28	Systems with Random Impurities
	29	Critical Droplets, Alias Instantons, and Metastability
		Appendix: Small Oscillations about the Instanton
	30	Renormalization and Scaling for Critical Phenomena
	31	Phase Space Path Integral
	32	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
Author Index
Subject Index
Supplements