
PATH INTEGRALS IN QUANTUM MECHANICS, STATISTICS, AND POLYMER PHYSICS. by Hagen Kleinert, World Scientific Publ. Co., 1990, pp xxi + 664. ISBN 9810201966; QC174.17.P27K54. Price: $86.00 hc ($24.00 pbk). 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, nontrivial modifications are required for Coulomb or centrifugallike 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 nonequilibrium 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 (published in Physics in Canada, September 1993, p. 308) 

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