Riassunto:
Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics 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. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of 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. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Contenuti:
VOLUME 1
Path Integrals in Classical Theory
Brownian motion: Introduction to the concept of path integration
Wiener path integrals and stochastic processes
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 generalizations
Appendices
Bibliography
Index
VOLUME 2
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 the path integral approach
Path integrals in the theory of gravitation, cosmology and string theory: advanced applications of path integrals
Path Integrals in Statistical Physics
Basic concept of statistical physics
Field theory at non-zero temperature
Superfluidity, superconductivity, non-equilibrium statistical physics in the path integral formalism and stochastic quantization
Path integrals formalism and lattice systems
Supplements
Bibliography
Index
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