Synopses & Reviews
A book of techniques and applications, this text defines the path integral and illustrates its uses by example. It is suitable for advanced undergraduates and graduate students in physics; its sole prerequisite is a first course in quantum mechanics. For applications requiring specialized knowledge, the author supplies background material.
The first part of the book develops the techniques of path integration. Topics include probability amplitudes for paths and the correspondence limit for the path integral; vector potentials; the Ito integral and gauge transformations; free particle and quadratic Lagrangians; properties of Green's functions and the Feynman-Kac formula; functional derivatives and commutation relations; Brownian motion and the Wiener integral; and perturbation theory and Feynman diagrams.
The second part, dealing with applications, covers asymptotic analysis and the calculus of variations; the WKB approximation and near caustics; the phase of the semiclassical amplitude; scattering theory; and geometrical optics. Additional topics include the polaron; path integrals for multiply connected spaces; quantum mechanics on curved spaces; relativistic propagators and black holes; applications to statistical mechanics; systems with random impurities; instantons and metastability; renormalization and scaling for critical phenomena; and the phase space path integral.
Synopsis
This text defines the path integral and illustrates its uses by example. Suitable for advanced undergraduates and graduate students, its sole prerequisite is a first course in quantum mechanics. The first part develops the techniques of path integration. Numerous considerations include vector potentials, functional derivatives and commutation relations, and perturbation theory and Feynman diagrams. The second section, dealing with applications, covers a host of situations, including those related to the WKB approximation and near caustics, scattering theory, relativistic propagators and black holes, instantons and metastability, and the phase space path integral. 1981 ed. Indexes. 26 figures.
Synopsis
This text for upper-level undergraduates and graduate students defines the path integral and shows by example how it can be used. The first part helps students develop techniques, and the second part offers detailed examples of several applications.
Synopsis
Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and dealsand#160;with applications, covering a host of illustrative examples.and#160;26 figures. 1981 edition.
Synopsis
Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.
Table of Contents
Part I Introduction
and#160; 1 Introduction and Defining the Path Integral
and#160;and#160;and#160; Appendix: The Trotter Product Formula
and#160; 2 Probabilities and Probability Amplitudes for Paths
and#160; 3 Correspondence Limit for the Path Integral (Heuristic)
and#160;and#160;and#160; Appendix: Useful Integrals
and#160; 4 Vector Potentials and Another Proof of the Path Integral Formula
and#160; 5 The Ito Integral and Gauge Transformations
and#160; 6 Doing the Integral: Free Particle and Quadratic Lagrangians
and#160;and#160;and#160; Appendix: Exactness of the Sum over Classical Paths
and#160; 7 Properties of Green's Functions; the Feynman-Kac Formula
and#160; 8 Functional Derivatives and Commutation Relations
and#160; 9 Brownian Motion and the Wiener Integral; Kac's Proof
and#160; 10 Perturbation Theory and Feynman Diagrams
Part II Selected Applications of the Path Integral
and#160; 11 Asymptotic Analysis
and#160; 12 The Calculus of Variations
and#160; 13 The WKB Approximation and its Application to the Anharmonic Oscillator
and#160; 14 Detailed Presentation of the WKB Approximation
and#160; 15 WKB Near Caustics
and#160; 16 Caustics and Uniform Asymptotic Approximations
and#160; 17 The Phase of the Semiclassical Amplitude
and#160; 18 The Semiclassical Propagator as a Function of Energy
and#160; 19 Scattering Theory
and#160; 20 Geometrical Optics
and#160; 21 The Polaron
and#160; 22 Spin and Related Matters
and#160;and#160;and#160; 22.1 The Direct Method-Product Integrals or Time Ordered Products
and#160;and#160;and#160; 22.2 Continuous Models for Spin
and#160; 23 Path Integrals for Multiply Connected Spaces
and#160;and#160;and#160; 23.1 Particle Constrained to a Circle
and#160;and#160;and#160; 23.2 Rudiments of Homotopy Theory
and#160;and#160;and#160; 23.3 Homotopy Applied to the Path Integral
and#160;and#160;and#160; 23.4 Extensions of Symmetric Operators
and#160; 24 Quantum Mechanics on Curved Spaces
and#160; 25 Relativistic Propagators and Black Holes
and#160; 26 Applications to Statistical Mechanics
and#160; 27 Coherent State Representation
and#160; 28 Systems with Random Impurities
and#160; 29 Critical Droplets, Alias Instantons, and Metastability
and#160;and#160;and#160; Appendix: Small Oscillations about the Instanton
and#160; 30 Renormalization and Scaling for Critical Phenomena
and#160; 31 Phase Space Path Integral
and#160; 32 Omissions, Miscellany, and Prejudices
and#160;and#160;and#160; 32.1 Field Theory
and#160;and#160;and#160; 32.2 Uncompleting the Square
and#160;and#160;and#160; 32.3 Rubber: Path Integral Formulation of a Polymer as a Random Walk
and#160; 32.4 Hard Sphere Gas Second Virial Coefficient
and#160; 32.5 Adding Paths by Computer
and#160; 32.6 A Perturbation Expansion Using the Path Integral
and#160; 32.7 Solvable Path Integral with the Potential ax2 + b/x2
and#160; 32.8 Superfluidity
and#160; 32.9 Fermions
and#160; 32.10 Books and Review Papers on Path Integrals
Author Index
Subject Index
Supplements