A Review for Mathematicians

Quantum Field Theory for Mathematicians

"It is often deeper to know why something is true rather than to have a proof that it is true."

From a review for the American Mathematical Society by Paul Federbush, a professor of mathematical physics at the University of Michigan.

This book has a lot to offer—to the right readers. It is an introduction to the most sophisticated and basic area of science, a field that is most elegant and awe-inspiring. In part quantum field theory involves the most tested truths in nature, predicting some experiments accurate to one part in 10 to the 19! In part it embraces string theory, where beauty and naturalness so far are the substitutes for any experimental verification.

The book has more breadth than usual texts on the subject, which are typically written for particle physicists. Here there is much more attention to applications in condensed matter physics, topics such as the quantum Hall effect, superconductivity, and superfluidity. Even in particle physics there are discussed many further developments such as grand unification, quantum gravity, string theory, again more topics than in the usual text. One can browse in this book to acquire enough familiarity with the common knowledge in the physics community to be comfortable in many physics colloquia.

There is a joy in the presentation. Many interesting anecdotes dot the text, charming stories about the developers of the subject. And the emphasis is on the little “physics” arguments that let one see why something is true. It is often deeper to know why something is true rather than to have a proof that it is true. The book is for physicists, or for the rare mathematician that can, when required, think like a physicist.