Book Review at AMAZON.com

on the first edition PATH INTEGRALS IN QUANTUM MECHANICS, STATISTICS, AND POLYMER PHYSICS . by Hagen Kleinert, World Scientific Publ. Co., 1990, pp xxi + 664. ISBN 9-81020-1966; QC174.17.P27K54. Price: $86.00 hc ($24.00 pbk).

One of The only TWO Books to own on PI's, March 9, 2001

Reviewer: Tim Hatamian from New York, NY USA

Kleinert the physicist is NOTHING short of phenomenal. This book is just one of his many treatises. After reading Feynman(+Hibbs) this is the text to follow up. . . .

Be sure to get the partial ERRATA for the text from this site.

click on the Kleinert's forum. There, you can also ask your questions regarding this text.

Kleinerts Completeness, June 26, 2000

Reviewer: Frank Witte from Utrecht, Netherlands

Kleinerts book "Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics" presents the reader with a very complete and very thorough discussion of path integration. The book offers such a wealth of topics,it becomes straightforward to select material, both for advanced undergraduate as well as graduate courses in theoretical physics.

Many, many issues dealt with in this volume have appeared here for the first time, such as the inclucion of the quantum mechanics of the hydrogen atom through path integrals. This book is a major step towards bringing this approach to quantum physics onto the same educational footing as the Schrvdinger equation that standard texts focus on. This book profits from the clarity and conciseness that is also a hallmark of Kleinerts scientific papers.

I would say this volume is highly recommendable for any student considering to major in {theoretical} physics, and an absolute must for any lecturer in this area. Infact, I don't know of any excuse not to have your own copy.

Review from Physics in Canada, September 1993, p. 308

Nobody possibly is better suited to write a book about path integrals than Hagen Kleinert. He contributed extensively to the method. Feynman, who pioneered the technique, stopped teaching the path integral approach to quantum mechanics when he realized that he could not solve, by this technique, such a fundamental problem as the hydrogen atom. He suggested the problem to Kleinert who finally did solve it. The usual definition of the Feynman path integral is not valid for all Hamiltonians. In particular, non-trivial modifications are required for Coulomb or centrifugal-like potentials.

In addition to covering these subjects in great detail, the technique is applied to polymer physics (effect of topological restrictions such as in entanglement problems), tunneling and non-equilibrium processes.

This is an advanced textbook, rigorous, thorough and complete. It starts from basic principles, but some familiarity with the concept of path integrals is necessary from treatments emphasizing a physically more intuitive approach. These can be found, for instance, in A. Feynman's own 1965 textbook with A.A. Hibbs, Quantum Mechanics and Path Integrals, or in a good Quantum mechanics book like Sakurai's Modern Quantum Mechanics.

B. Joos
Department of Physics University of Ottawa