Quantum Field Theory and the Standard Model, Matthew D. Schwartz, Cambridge U. Press, 2014. $90.00 (850 pp.). ISBN 978-1-107-03473-0
Well before two research teams at CERN’s Large Hadron Collider announced the discovery of a Higgs-like boson, the standard model of particle physics had been validated by data collected across a broad range of energies. Theory—in particular, the formulation of the standard model as a relativistic quantum field theory (QFT)—played a significant role in that success. To be sure, a QFT is an abstract and highly mathematical construct, but it offers a calculational framework from which can be derived predictions that can be tested to high precision.
To this day, QFTs are the primary theoretical tools for advancing the frontiers of knowledge about the basic principles underlying the behavior of matter. For that reason, it is important that the theories be presented in a modern context. That’s what Matthew Schwartz’s Quantum Field Theory and the Standard Model attempts to do. The voluminous text provides an inspiring tour of theoretical particle physics, from the very basics, to the detailed formulation of the standard model, to advanced concepts of present-day research. The book is at a level appropriate for students who have had a solid undergraduate course in quantum mechanics. The overall format of relatively short sections, underlined headings with large fonts, and highlighted boxes helps to make the book user friendly. A bit annoying, though, is the lax handling of upper and lower Lorentz indices, which sometimes leads to confusion.
Schwartz, an associate professor at Harvard University, is an experienced researcher and an expert in applying QFT to experiments for testing the standard model. His book covers the grand ideas that feed into the standard model: relativistic QFTs, including gauge theories; symmetries; and symmetry breaking. But consistent with the spirit of Schwartz’s research, it is a pragmatic text that primarily focuses on the theory’s perturbative aspects, teaching ideas and methods of relativistic QFTs so that the reader can perform practical calculations.
Quantum Field Theory and the Standard Model moves from the fundamental Lorentz symmetry to the various kinds of fields and particles and their interactions in the Lagrangian and Hamiltonian approaches. It discusses perturbation theory, Feynman diagrams, the path-integral formulation, loop calculations and renormalization, broken and unbroken gauge theories, and tests of quantum chromodynamics and the electroweak theory—the sectors of the standard model that describe the strong force and electromagnetic-plus-weak forces respectively. The last part of the book is concerned with more advanced topics, such as heavy-quark effective theory and soft-collinear effective theory, which are important in current standard-model tests in flavor physics and at high-energy colliders. Schwarz’s introduction to them will be useful for more sophisticated readers. Throughout, the author maintains the connection between theory and experiment; he also includes interesting historical references.
The book is full of explicit derivations and concrete calculations that will allow readers to dig into the subjects, provided they are willing to invest sufficient time. Its derivation of Feynman graphs through the Hamiltonian formulation, for example, shows the pedagogically helpful relationship between the Feynman graphs and the conventional perturbation theory of nonrelativistic quantum mechanics. The more formal Lagrangian and path-integral approaches, on the other hand, are more elegant and efficient pathways to that central tool of particle physics.
Quantum Field Theory and the Standard Model may be considered a successor to Michael Peskin and Daniel Schroeder’s An Introduction to Quantum Field Theory (Westview Press, 1995), which for almost 20 years has been a standard reference. Schwartz’s book is similar in its selection of themes and presentation, yet with more details, different viewpoints, and broader introductory material. Unlike Peskin and Schroeder’s, it covers new developments and modern topics, including spinor-helicity methods, heavy-quark effective theory, and soft-collinear effective theory, and it offers a modern point of view on the use and relevance of nonrenormalizable theories. Schwartz’s section about tests of the standard model includes the recently measured Higgs boson properties in electroweak precision tests. That discussion, however, does not go beyond the one-loop level and gives the misleading impression that one-loop calculations are sufficient to get agreement between theory and experiment. In fact, important higher-order calculations not discussed by Schwartz have been done in the past two decades.
Overall, Quantum Field Theory and the Standard Model is a balanced and comprehensive text. I recommend it for beginners in particle physics and its theoretical foundations. Containing a rich collection of information in a single volume, it will also be a useful reference for lecturers and researchers.
Wolfgang Hollik is director of the theory group at the Max Planck Institute for Physics in Munich, Germany, and honorary professor at the Technical University of Munich. His research interests include the phenomenology of the standard model and precision calculations for physics at high-energy colliders.
