By Marcos Mariño
Cambridge University Press
Intended to be a fundamental resource for graduate students in particle, theoretical and mathematical physics, the book gives a highly pedagogical introduction to some advanced topics of quantum field theory (QFD).
The standard approach to QFD, one of the pillars of modern physics, is the perturbative one. Although successful, it is not sufficient to address many important phenomena. In this book, the author gives an introduction to two methods that go beyond the standard perturbative framework: instantons and large-N expansion.
The first part of the volume offers a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large-order behaviour of perturbation theory, and Yang–Mills theories. In the second part, large-N expansion in QFT is examined.
The topics are presented in a well-organised form, and each subject is explained with detailed mathematical derivations and then illustrated with a model or example in which it is implemented. This enables students to move easily through the text and gain practical experience with the most important tools of the field.
Apart from the basic building blocks in the theory of instantons and of large-N expansion, the choice of topics has been dictated by the author’s taste and expertise, as he himself admits. As a consequence, some subjects covered extensively elsewhere in the literature are left aside, while space has been given to topics not commonly treated in textbooks. Moreover, supersymmetry has been avoided as much as possible, by choice.
