Grosche Christian, Steiner Frank. Handbook of Feynman Path Integrals

Springer-Verlag Berlin Heidelberg, 1998. — 457 p.The book follows the general idea as originally conceived. Chapters 1-5 have the character of a textbook and give a self-contained, and up-to-date
introduction to the theory of path integrals for those readers who have not yet studied path integrals, but have a good knowledge of the fundamentals
of quantum mechanics as covered by standard courses in theoretical physics. Chapter 6 makes up the largest part of this Handbook and contains a rather complete table of path integrals in non-relativistic quantum mechanics, including supersymmetric quantum mechanics, and statistical mechanics. To each path integral listed in the table we attach a comprehensive list of references which altogether make up almost 1000 references. The Introduction in Chap. 1 is mainly of a historical nature and gives the reader some insight into the remarkable development of Feynman's path integral approach. Since some of the historical facts are not so well known we thought it would be worthwhile to present them in Chap. 1.General Theory
The Feynman Kernel and the Green Function
The Path Integral in Cartesian Coordinates
Gaussian Path Integrals and Zeta Function Regularization
Evaluation of Path Integrals by Fourier Series
Path Integration Over Coherent States
Fermionic Path Integrals
The Path Integral in Spherical Coordinates
The Path Integral in General Coordinates
Transformation Techniques
Exact Path Integral Treatment of the Hydrogen Atom
The Path Integral in Parabolic Coordinates
Basic Path Integrals
The Free Particle
The Quadratic Lagrangian
The Radial Harmonic Oscillator
Path Integration Over Group Manifolds
Perturbation Theory
Path Integration and Perturbation Theory
Summation of the Perturbation Series for d- and d'-Potentials
Partition Functions and Effective Potentials
Semiclassical Expansion About the Harmonic Approximation
Semiclassical Theory
Semiclassical Theory and Quantum Chaos
Semiclassical Expansion of the Feynman Path Integral
Semiclassical Expansion of the Green Function
The Gutzwiller Trace Formula
Table of Path Integrals
General Formulae
The General Quadratic Lagrangian
Discontinuous Potentials
The Radial Harmonic Oscillator
The Poschl-Teller Potential
The Modified Poschl-Teller Potential
Motion on Group Spaces and Homogeneous Spaces
Coulomb Potentials
Magnetic Monopole and Anyon Systems
Motion in Hyperbolic Geometry
Explicit Time-Dependent Problems
Point Interactions
Boundary Value Problems
Coherent States
Fermions
Supersymmetric Quantum Mechanics