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Techniques and Applications of Path Integrationby L. S. Schulman
Synopses & ReviewsPublisher Comments: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 FeynmanKac 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: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. 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. Synopsis:This text for upperlevel 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: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. Table of ContentsPart 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 FeynmanKac 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 MethodProduct 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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