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Techniques and Applications of Path Integration

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Techniques and Applications of Path Integration Cover

 

Synopses & Reviews

Publisher 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 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:

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 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:

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 Contents

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

Product Details

ISBN:
9780486445281
Author:
Schulman, L. S.
Publisher:
Dover Publications
Author:
Physics
Subject:
Physics
Subject:
Quantum Theory
Subject:
Mathematical Physics
Subject:
Path integrals
Subject:
Physics-Quantum Mechanics
Edition Description:
Trade Paper
Series:
Dover Books on Physics
Publication Date:
20051231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
448
Dimensions:
8.5 x 5.38 in 1.02 lb

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Product details 448 pages Dover Publications - English 9780486445281 Reviews:
"Synopsis" by ,
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" by ,
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" by ,
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" by ,
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.

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