Techniques and Applications of Path Integration Book

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