Path Integrals in Physics

Abstract

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 inHamiltonian 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. Pathintegrals over anticommuting variables for fermions and generalisations. Appendices. Bibliography. Index.Volume 2: 3. Quantum Field Theory: the Path Integral Approach. Path integral formulation of the simplest quantum field theories. Path integral quantization of gauge field theories. Non-perturbative methods for the analysis of quantum field models in thepath integral approach. Path integrals in the theory of gravitation, cosmology and string theory: advanced applications of path integrals. 4. Path Integrals in Statistical Physics. Basic concept of statistical physics. Field theory at non-zerotemperature. Superfluidity, superconductivity, non-equilibrium statistical physics in the path integral formalism and stochastic quantization. Path integrals formalism and lattice systems. Supplements. Bibliography. Index