Techniques and Applications of Path Integration

Overview

Emphasizes the many applications that have been found for path integrals in quantum mechanics, statistical physics, field theory, and optics. Covers both the Feynman integral of quantum mechanics and the Wiener integral of probability theory. Initial experience is gained with solvable integrals and some of the formal and general properties developes.
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Techniques and Applications of Path Integration

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Overview

Emphasizes the many applications that have been found for path integrals in quantum mechanics, statistical physics, field theory, and optics. Covers both the Feynman integral of quantum mechanics and the Wiener integral of probability theory. Initial experience is gained with solvable integrals and some of the formal and general properties developes.
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Product Details

  • ISBN-13: 9780486445281
  • Publisher: Dover Publications
  • Publication date: 12/27/2005
  • Series: Dover Books on Physics Series
  • Pages: 448
  • Product dimensions: 5.30 (w) x 8.40 (h) x 0.90 (d)

Table of Contents

1 Introducing and Defining the Path Integral 3
Appendix: The Trotter Product Formula 9
2 Probabilities and Probability Amplitudes for Paths 13
3 Correspondence Limit for the Path Integral (Heuristic) 16
Appendix: Useful Integrals 20
4 Vector Potentials and Another Proof of the Path Integral Formula 22
5 The Ito Integral and Gauge Transformations 27
6 Doing the Integral: Free Particle and Quadratic Lagrangians 31
Appendix: Exactness of the Sum over Classical Paths 39
7 Properties of Green's Functions; the Feynman-Kac Formula 42
8 Functional Derivatives and Commutation Relations 49
9 Brownian Motion and the Wiener Integral; Kac's Proof 53
10 Perturbation, Theory and Feynman Diagrams 65
11 Asymptotic Analysis 73
12 The Calculus of Variations 79
13 The WKB Approximation and its Application to the Anharmonic Oscillator 92
14 Detailed Presentation of the WKB Approximation 108
15 WKB Near Caustics 118
16 Caustics and Uniform Asymptotic Approximations 131
17 The Phase of the Semiclassical Amplitude 143
18 The Semiclassical Propagator as a Function of Energy 147
19 Scattering Theory 158
20 Geometrical Optics 164
21 The Polaron 170
22 Spin and Related Matters 182
23 Path Integrals for Multiply Connected Spaces 190
24 Quantum Mechanics on Curved Spaces 214
25 Relativistic Propagators and Black Holes 225
26 Applications to Statistical Mechanics 237
27 Coherent State Representation 242
28 Systems with Random Impurities 259
29 Critical Droplets, Alias Instantons, and Metastability 271
Appendix: Small Oscillations about the Instanton 284
30 Renormalization and Scaling for Critical Phenomena 290
31 Phase Space Path Integral 303
32 Omissions, Miscellany, and Prejudices 315
Author Index 349
Subject Index 353
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