# Gasp with Awe and Laugh with Joy!

## "The exposition is colloquial, in the style of somebody at the blackboard talking to a small class of bright students, flavoring the discussion with relevant and amusing anecdotes."

From a review published in Foundations of Physics of my textbook on modern quantum field theory by O. W. Greenberg, a professor of physics at the University of Maryland.

Anthony Zee is a talented and imaginative expositor who has written three

popular books on physics and cosmology. He is also a talented and imaginative

physicist who has an unusually broad range of interests. In this book Zee deploys

his imaginative style as a writer in the service of his incisive understanding of

physics to produce a unique book on quantum field theory. Quantum field theory

in a nutshell in more than 500 pages sounds like an oxymoron, but Zee’s book lives

up to the title, although we should think of the nutshell as a large pomegranate

with many piquant seeds inside.

Zee gets off to a fast start by introducing the Feynman path integral using the

limit of a double slit experiment with more and more holes and then more and

more screens. By page 15 he has shown how to calculate Gaussian integrals over n

variables with external sources, explained the gist of Wick’s theorem and of the

steepest descent approximation. He gives simple arguments to show why like

electric charges repel and masses attract. Still within Part I he calculates

the Planck mass in extra dimensions in terms of the four-dimensional Planck mass

and the compactification radius, outlines canonical quantization, gives Feynman

rules for scalar Phi4 theory, outlines a simplified calculation of the Casimir effect,

derives Noether’s theorem, and finishes by giving the rationalized

action for a scalar particle in a gravitational field.

Zee doesn’t slow down in the rest of the book. Rather than give a laundry list of

all the other topics he treats, I will first highlight a discussion I particulary like,

and then make some general comments. In discussing quantum electrodynamics

Zee absorbs the electric charge in the vector potential so that the charge enters the

photon propagator rather than the electron-positron-photon vertex. This

automatically leads to having the renormalized charges equal if their bare charges

are equal and makes the electron field strength renormalization constant equal the

vertex renormalization constant (sometimes called Z2 and Z1) equal, a fact that

usually requires a detailed argument.

The exposition is colloquial, in the style of somebody at the blackboard talking to

a small class of bright students, flavoring the discussion with relevant and amusing

anecdotes. The explanations, while succinct, are understandable. The exercises

lead to further development of topics in the text. Topics not usually presented in a

first text on quantum field theory find their rightful place; in particular

applications to collective phenomena and condensed matter, such as critical

phenomena (but only Landau-Ginzburg mean field theory), the integer and fractional

quantum Hall effects, and Anderson localization are included. The general

philosophy is effective field theory and the associated emphasis on symmetry and

the renormalization group. Some topics, such as Hawking radiation, will have to

be augmented by the instructor if included in a course, but by and large the book

is self contained. Appendices include a user’s guide to group theory and, most

welcome, a discussion of van der Waerden’s undotted and dotted indices for

spinors.

Who is the audience for this book? First of all, any physicist or mathematician

who wants an intuitive introduction to quantum field theory. Working theoretical

physicists will find it useful both as a quick introduction to topics they don’t know

and as a source of novel and pithy explanations of topics they do know. Working

experimental physicists will find it useful to bridge the gap between theory and

experiment. Students will find it an inspiring, if at times a bit intimidating, text

on quantum field theory in all its guises. For use as a text in a field theory course

oriented toward particle physics, a supplementary text such as the book by Peskin

and Schroeder would be helpful. The best way to capture the spirit of this book is

to quote Zee quoting his advisor Sidney Coleman that quantum field theory made

“the spectator gasp with awe and laugh with joy.” Zee has conveyed that awe and

joy in this book.