next up previous
Next: About this document

For email orders of the book click this URL. Price $38 (approx 50 DM)!

This is the blurb as it appears on the cover of the book.

H. Kleinert


in Quantum Mechanics, Statistics,
and Polymer Physics

World Scientific Publishing Co., Singapore 1995.

This is the second, significantly expanded edition of the comprehensive textbook of 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular of the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r- and 1/r^2-potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion.

The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation expansion. In contrast to ordinary perturbation expansions, divergencies are absent. Instead, there is a uniform convergence from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals.

Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory now also applies to small orders.

Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics ( anyons) is introduced and applied to explain the fractional quantum Hall effect.


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.

The present edition appeared first in German under the title PFADINTEGRALE in Quantenmechanik, Statistik und Polymerphysik, B.I.-Wissenschaftsverlag, Mannheim, 1993.

To order the book from the publishing company click this line!
To List of Books and Articles

----> Back to HOMEPAGE of this server
----> Go to MASTER INDEX of this server