The standard model for beginners

The 2000-year quest to find nature’s basic building blocks, which began with Democritus’s atomic hypothesis, has culminated in the quantum field theory (QFT) known as the standard model of particle physics. The standard model vastly outperforms its unpretentious name: It is a self-consistent mathematical theory of quarks and leptons, which make up all ordinary matter, and their fundamental interactions. It provides the basic rules that govern elementary particles, atoms, molecules, and even living things.

In his new book, Quantum Field Theory, as Simply as Possible, theoretical physicist A. Zee provides an overview of QFT aimed at both aspiring theorists who haven’t yet taken their first course on the subject and dedicated laypeople who remember high school math and are willing to grapple with the book’s heady concepts. As the title suggests, this volume is not for everyone. But those readers who are willing to think deeply will be rewarded with a rich conceptual understanding and appreciation of what Zee somewhat hyperbolically calls the “greatest monument to the human intellect.” For example, they’ll understand that all electrons—and, for that matter, all other particle species—are truly identical because they are described by a single quantum field. Sweet.

Zee’s book is divided into six parts. Each contains a preview, three to six bite-size chapters, and a recap. He leads readers on a journey that generally proceeds chronologically through the history of physics, from the time of Galileo Galilei and Isaac Newton to the present. Part 1 begins with the physics of forces and particles and ends with spacetime and special relativity.

Part 2 opens with the Euler–Lagrange formulation of classical mechanics, which is followed by a discussion of the action principle and the path-integral formulation of quantum mechanics. Diving deep into the path-integral approach is a big plus for a book that is conceptual and not computational, because it beautifully connects classical and quantum physics. Zee impressively succeeds in conveying the essence of the approach without drowning readers in complex mathematics: He only asks readers to remember what integrals are.

Parts 3 and 4 are the heart of the book. They begin with a discussion of force carriers, before moving on to quantum fields, quantum electrodynamics, and Yang–Mills gauge theory. After successfully navigating those parts, the reader will be a conceptual quantum field theorist—or, at the very least, will appreciate the majesty of QFT.

Part 5 pushes the audience to its limits and discusses two triumphs of QFT: antimatter and the standard model. It also discusses quantum field theorists’ unfulfilled aspirations to create a Grand Unified Theory that describes all the standard model’s forces. Zee then gives readers a bonus by describing Albert Einstein’s general relativity—even though it is not a QFT—and the challenges of quantizing gravity. He ends the book with a cooldown in part 6, which compares QFT with quantum mechanics and assesses QFT’s intellectual completeness and its shortcomings.

Beyond the clarity of his explanations, his illuminating conceptual diagrams, and his boxed bits of wisdom, Zee has a strong voice that makes the long journey both interesting and personal. It comes out in anecdotes, historical passages—many of which are based on Zee’s recollections—footnotes, and endnotes. He includes wonderful stories about giants that we know and he worked with, including Richard Feynman, Julian Schwinger, Sheldon Glashow, and Steven Weinberg; but he also includes depictions of physicists who are less well known, such as his PhD adviser, the late Sidney Coleman, who was the premier quantum field theorist of his generation.

Despite its breadth, there are things you won’t find in Zee’s book. Although he mentions the Higgs mechanism, Zee doesn’t discuss the Higgs boson, its discovery, or its mass—or, for that matter, the mass of any other particle. Save for a few speculations about grand unified theories, which occupied a significant part of his own research, Zee sticks to what has been established: Unlike many popular books about particle physics, he eschews any discussion of string theory and the multiverse.

Quantum Field Theory, as Simply as Possible is a theorist’s account of the rise of the standard model. Zee is the ideal person to tell that story, as his career coincided with the triumph of QFT, and he was an important participant in its development. Whether or not readers agree that QFT is humanity’s greatest intellectual achievement, they will come away with a deeper understanding of theoretical physics, an appreciation of what QFT is, and an esteem for its elegance.

Michael S. Turner is a visiting professor at the University of California, Los Angeles, and the Bruce V. and Diana M. Rauner Distinguished Service Professor Emeritus at the University of Chicago.