Path Integrals in Quantum Mechanics Statistics and Polymer Physics - Hardcover

Hagen Kleinert

Hardcover

ISBN 10: 9810214715 ISBN 13: 9789810214715

Publisher: World Scientific Pub Co Inc, 1995

Synopsis

This textbook on the theory and applications of path integrals contains the solution to a number of non-trivial path integrals, most notably that of the Coulomb system. This has become possible by finding a consistent formulation of path integrals in spaces with curvature and torsion. 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 tunnelling problems are analyzed in detail. Their relevance to superconductivity and the large-order behaviour of perturbation expansions is demonstrated. The path integral description of equilibrium thermodynamics is presented, and an extension to non-equilibrium processes is presented. 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. Now in its second edition, the book has been extended by a more powerful variational approach which can now be applied to excited states and to tunnelling processes through high as well as low barriers. With it, the known large-order perturbation theory has been continued down to small orders. The book contains a detailed non-abelian Chern-Simons theory of polymer entanglement in terms of HOMFLY-polynomials and a discussion of anyonic aspects of the fractional quantum Hall effect and of high-Tc superconductivity. The semiclassical analysis incorporates now multidimensional systems to establish contact with recent work on chaos.

About this title

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

Review

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

Edition details

• Publisher: World Scientific Pub Co Inc
• Publication date: 1995
• ISBN 10: 9810214715
• ISBN 13: 9789810214715
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 920