Feynman integrals in theoretical, nuclear and statistical physics.

*(English)*Zbl 0712.58001
Monographs and Textbooks in Physical Science, Lecture Notes, 1414. Napoli: Bibliopolis. xvii, 265 p. (1989).

This book originates in a series of lectures and seminars given at the Graduate School in Physics of the University of Genova and at the Physics Department of the University of Napoli. The central aim of the authors is to show how the functional integral formalism can be used as a “unifying tool” for very different physical problems, from elementary particles to nuclear physics, statistical mechanics and condensed matter.

The basic ideas of Feynman’s Integral together with the necessary formalism are presented in the first four chapters. The first application is given in Chapter 5, where the problem of the polaron is discussed. The traditional methods, i.e. perturbative approximation and canonical transformation are both explained from a critical point of view.

The applications of Feynman’s Integral to the Nuclear Physics are given in Chapter 6 and they refer to the evaluation of static properties of nuclei, the nonequilibrium properties like the barrier penetration, the spontaneous fission, etc.

In Chapter 8 it is presented the Meson Exchange Currents problem, i.e. the problem to describe properly the electromagnetic interactions of nuclei. Some basic results are derived within a euclidean version of theory, and the concept of instanton is then introduced (Chapter 9). The topic of conservation laws and quantization of gauge fields necessary for the two last chapters is contained in Chapter 7.

The book is of a real interest both for nuclear physicists and solid state theorists giving a description of the language and of the methods of field theory in a unified way.

The basic ideas of Feynman’s Integral together with the necessary formalism are presented in the first four chapters. The first application is given in Chapter 5, where the problem of the polaron is discussed. The traditional methods, i.e. perturbative approximation and canonical transformation are both explained from a critical point of view.

The applications of Feynman’s Integral to the Nuclear Physics are given in Chapter 6 and they refer to the evaluation of static properties of nuclei, the nonequilibrium properties like the barrier penetration, the spontaneous fission, etc.

In Chapter 8 it is presented the Meson Exchange Currents problem, i.e. the problem to describe properly the electromagnetic interactions of nuclei. Some basic results are derived within a euclidean version of theory, and the concept of instanton is then introduced (Chapter 9). The topic of conservation laws and quantization of gauge fields necessary for the two last chapters is contained in Chapter 7.

The book is of a real interest both for nuclear physicists and solid state theorists giving a description of the language and of the methods of field theory in a unified way.

Reviewer: G.Zet

##### MSC:

58-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis |

58Z05 | Applications of global analysis to the sciences |

81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |

58D30 | Applications of manifolds of mappings to the sciences |

82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |