Techniques and applications of path integration.

*(English)* Zbl 0587.28010
A Wiley-Interscience Publication. New York etc.: John Wiley & Sons, Inc. XV, 359 p. (1981).

This is an interesting and extremely readable book on path integrals. The level of mathematical rigour is rather variable, but the book is full of physical insights. The contents are largely a reflection of the author’s own research interests. Nevertheless the selected applications, which are treated, cover a broad spectrum of theoretical physics. These applications include such diverse topics as the WKB approximation (treated from a functional integral viewpoint), spin and related matters, path integrals for multiply connected and curved spaces, black holes (Hartle and Hawking’s path integral derivation of the elements of black hole thermodynamics), together with further applications to statistical mechanics, coherent states, systems with random impurities, critical droplets, renormalization and scaling for critical phenomena. There is a (more mathematical) introduction on defining and calculating functional integrals and a miscellaneous section dealing with omissions. The most significant omission is inevitably the application of functional integrals to gauge theories, but the material here is so extensive that this would require a separate book. Altogether this is an excellent introductory book on the formal methods and applications of path integration, suitable for graduate students and research workers wishing to know more about functional integrals in theoretical physics.

##### MSC:

28C20 | Set functions and measures and integrals in infinite-dimensional spaces |

81S40 | Path integrals in quantum mechanics |

28-02 | Research monographs (measure and integration) |

81-02 | Research monographs (quantum theory) |

58D30 | Spaces and manifolds of mappings in applications to physics |