Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics - Softcover

Kleinert, Hagen

9789810201975: Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics

Softcover

ISBN 10: 9810201974 ISBN 13: 9789810201975

Publisher: World Scientific Publishing Company, 1990

This comprehensive textbook on the theory and applications of path integrals is the first to contain the solutions to a number of non-trivial path integrals, most notably of the Coulomb system. It has become possible by finding a consistent formulation of path integrals in spaces with curvature and torsion, presented here also for the first time. Special emphasis is given to stability problems of path fluctuations in the presence of singular potentials such as centrifugal and angular barriers. The limitations of Feynman's time slicing procedure are exhibited and a new path integral formula is found which avoids the frequent danger of path collapse. The physically important applications to tunneling problems are analyzed in detail. Their relevance to superconductivity and the large-order behavior of perturbation expansions is demonstrated. The path integral description of equilibrium thermodynamics is presented, and an extension to non-equilibrium processes is given. Much attention is paid to path integrals in spaces with topological restrictions. Their applications to entanglement problems in polymer physics and their relevance to particle statistics are discussed, also to the recently popular phenomenon of fractional statistics.

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About the Author:

Hagen Kleinert is Professor of Physics at the Freie Universit�t Berlin, Germany. As a visiting scientist, he has spent extended periods of time at CERN, the European Organization for Nuclear Research in Geneva; at the California Institute of Technology in Pasadena; at the Universities of California in Berkeley, Santa Barbara, and San Diego; at the Los Alamos National Laboratories in New Mexico; and at Princeton University, New Jersey. He has made numerous contributions to our understanding of particle physics, mathematical physics, condensed matter physics, chemical physics, and nuclear physics. His two-volume book Gauge Fields in Condensed Matter, published by World Scientific, develops a new quantum field-theory of phase transitions on the basis of disorder fields. Such fields have since become a powerful tool to investigate the statistical properties of fluctuating line-like excitations in various many-body systems such as superfluids, superconductors, and crystals.

Review:

Kleinert's book presents the reader with a very complete and very thorough discussion of path integration... -- Journal of Statistical Physics, Apr 2003

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