Comprehensive, detailed, and systematic, this volume presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. The book describes in detail various applications, including systems with Grassmann variables.

Volume 1: 1 Path Integrals in Classical Theory. Brownian motion: Introduction to the concept of parth integration. Wiener path integrals and stochastic processes. 2 Path integrals in Quantum Mechanics. Feynman path integrals. Path integrals in Hamiltonian formalism. Quantizations, the operator ordering problem and path integrals. Path integrals and quantizations in spaces with topologiecal constraints. Path integrals in curved spaces, space time transformations and the Coulomb problem. Path integrals over anticommuting variables for fermions and generalisations. Appendices. Bibliography. Index.