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Techniques and Applications of Path Integration

L. S. Schulman
Dover Publications
Publication Date: 
Number of Pages: 
We do not plan to review this book.

Part I
  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