Path Integrals in Physics : Volume I Stochastic Processes and Quantum Mechanics book cover
1st Edition

Path Integrals in Physics
Volume I Stochastic Processes and Quantum Mechanics

ISBN 9780367397142
Published September 11, 2019 by CRC Press
336 Pages

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Book Description

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.

Table of Contents

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


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Chaichian, M; Demichev, A


"In contrast to many other existing books on functional integral methods, this monograph introduces the path integral in an inductive way by studying the Brownian motion of a particle in a solvent. Indeed the Brownian motion is probably the best example of how to understand and acquire the concept of the path integral in the most natural way … The book will definitely be very helpful for teachers of the subject as a source of ideas on how to present concepts of functional integrals with their applications to their students … the monography can serve as a manual for almost an encyclopedia collection of information from both the physical subject and the bibliography in this field."
-Milan Noga

"The reader whose interest ranges across quantum, statistical, and stochastic field theories and their application to particle physics and condensed matter physics will find much to enjoy here. The applications are diverse, from the physics of macromolecules to Bose-Einstein condensation to quantization on non-commutative spaces. The explanations are clear, the details present without being overwhelming, and the equations support the text well, without being the impenetrable hedge that detail sometimes provokes … I found reading these books a comfortable and, on occasion, a familiar, experience."
-R. Rivers, University of London, UK