By Luciano Maiani and Omar Benhar
CRC Press
Quantum field theory (QFT) is the mathematical framework that forms the basis of our current understanding of the fundamental laws of nature. Its present formulation is the achievement of almost a century of theoretical efforts, first initiated by the necessity of reconciling quantum mechanics with special relativity. Its success is exemplified by the Standard Model, a specific QFT that spectacularly accounts for all of the observations performed so far in particle-physics experiments over many orders of magnitude in energy. Learning and mastering QFT is therefore essential for anyone who wants to understand how nature works on the smallest scales.
This book gives a concise and self-contained introduction to the basic concepts of QFT. As mentioned in the preface, it is mainly addressed to students with different interests who are approaching the subject for the first time, and is based on a series of lecture courses taught by the authors over the course of a decade at the University of Rome La Sapienza. Topics are selected and presented following their historical development and constant reference is made to those experiments that marked key advances, and sometimes breakthroughs, on the theoretical front. Some important subjects were not included, but they can be reconsidered later for more in-depth study.
The book is conceived as the first of a series that comprises two other texts on the more advanced topics of gauge theories and electroweak interactions (in collaboration with the late Nicola Cabibbo). The authors do not indulge in technical discussions of more formal aspects but try to derive the main physics results with the minimum amount of mathematical machinery. Although some concepts would have benefitted from a more systematic discussion, such as the scattering matrix and its definition through asymptotic states, the goal of giving an essential introduction to QFT and providing a solid foundation in this for the reader is achieved overall. The experience of the authors as both proficient teachers of the subject and main players is crucial to finding a good balance in establishing the QFT framework.
The first part of the book (chapters 1–3) is dedicated to a short review of classical dynamics in the relativistic limit. Starting from the principles of relativity and minimal action, the motion of point-like particles and the evolution of fields are described in their Lagrangian and Hamiltonian formulations. Special emphasis is given to symmetries and conservation laws. Quantisation is introduced in chapter 4 through the example of the scalar field by replacing the Poisson brackets with commutators of operators. Equal-time commutation rules are then used to define creation and destruction operators and the Fock space. Chapter 5 deals with the quantisation of the electromagnetic field. The approach is that of canonical formalism in the Coulomb gauge, but no mention is made of the complication due to the presence of constraints on fields. Chapters 6 and 7 are dedicated to the Dirac equation and the quantisation of the Dirac field. Besides introducing the usual machinery of spinors and gamma matrices, they include a detailed analysis of the relativistic hydrogen atom as well as concise though important discussions about Wigner’s method of induced representations as applied to the Lorentz group, micro-causality and the relation between spin and statistics. The propagation of free fields is analysed in chapter 8, while the three chapters that follow introduce the reader to relativistic perturbation theory. Chapter 12 discusses discrete symmetries (C, P and T) in QFT, gives a proof of the CPT theorem and illustrates its consequences. The last part of the book is dedicated to applications of QFT formalism to phenomenology. The authors give a detailed account of QED in chapter 14 by discussing a variety of physical processes. The reader is here introduced to the method of Feynman diagrams through explicit examples following a pragmatic approach. The following chapter deals with Fermi’s theory of weak interactions, again making use of several explicit examples of physical processes. Finally, chapters 13 and 16 are devoted to the theory and phenomenology of neutrinos. In particular, the last section discusses neutrino oscillations (both in a vacuum and through matter) and presents a thorough analysis of current experimental results. There is also a useful set of exercises at the end of each chapter.
Both the pragmatic approach and choice of topics make this book particularly suited for readers who want a concise and self-contained introduction to QFT and its physical consequences. Students will find it a valuable companion in their journey into the subject, and expert practitioners will enjoy the various advanced arguments that are scattered throughout the chapters and not commonly found in other textbooks.
