Path Integrals In Quantum Mechanics, Statistics, And Polymer Physics - Hardcover

Kleinert, Hagen

Hardcover

ISBN 10: 9810201966 ISBN 13: 9789810201968

Publisher: World Scientific Publishing Co Pte Ltd, 1990

Synopsis

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.

About this title

Review

"Kleinert's book presents the reader with a very complete and very thorough discussion of path integration... a new extensive and, again, rather complete chapter has been added on the use of path integration techniques in the analysis of financial markets. This chapter would do well in any high-level course on stochastic financial models and is a wonderful occasion for candidate mathematical and theoretical physicists to realize what great potential there hides still in the methodologies and techniques that have been developed... It profits from the clarity and conciseness that is also a hallmark of Kleinert's scientific papers... this volume is highly recoomendable for any student considering majoring in theoretical physics or chemistry, and an absolute must for any lecturer in this area... In fact, I don't know of any excuse not to have your own copy." Journal of Statistical Physics, Apr 2003"

About the Author

Hagen Kleinert is Professor of Physics at the Freie Universität 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.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 1990
• ISBN 10: 9810201966
• ISBN 13: 9789810201968
• Binding: Hardcover
• Language: English
• Number of pages: 688