Resources

Main sources.

  • David Tong's notes. Short, reasonably complete, highly recommended by math-adjacent physicists. Our main source.

  • Charles Torre's notes. Thorough, readable, good balance between math and physics language. Our main source for classical field theory (subject to change).

Main sources for "math perspective".

Textbooks, etc.

  • Quantum Field Theory and the Standard Model by Matthew Schwartz: the current "gold standard" of QFT textbook

  • An Introduction to Quantum Field Theory by Peskin and Schroeder: the previous gold standard, more condensed than Schwartz and famous for causing much graduate student anguish

  • Quantum Field Theory by Mark Srednicki. A more friendly resource, has been highly recommended to me. Takes a more path integral-oriented approach.

  • Excellent Cambridge Part III lecture notes by Dexter Chua: Quantum Field Theory (without loops) and Advanced Quantum Field Theory. Based on lectured by Allanach and Skinner, resp.

  • QFT in a Nutshell, by A. Zee. A mathematician-friendly QFT textbook in the "guided tour" style (but more complete than Folland's "QFT: a Tourist Guide for Mathematicians).

  • Introduction to Quantum Field Theory for Mathematicians, (student-compiled notes on a course by Michel Talagrand). What it says on the cover (but more analysis-heavy than our target level).

Higher-level Resources for Mathematicians (mostly more advanced than our scope but useful to look at)

When I first arrived in the states, at age 2, my family was visiting the Park City school on QFT where my dad was a participant. The introduction to the compiled notes had the following line:

"We can safely assert that the physical intuition physicists bring to bear on these problems, even in models whose relevance to the real world seems tenuous at best, has not yet penetrated at all into mathematics. "

This state of affairs has changed profoundly since then. QFT has permeated math to the extent where QFT-related texts oriented at mathematicians could fill up pages of bibliography. Here I will list a few that I have been recommended or think may be particularly useful to follow along with. I am also including several sources for physicists which I have been recommended.

  • The PCMI notes mentioned above feature an excellent short course by Jeff Rabin.

  • The 1996-97 IAS school on String Theory has a crazy amount of good and high-level material, including introductory material on quantum mechanics and field theory. I recommend looking at Ludwig Faddeev's course from the first semester. The book version of the school also has a nice text by Dan Freed and Deligne on Classical Field Theory.

  • The first few sections of Chapter 1 of this book by Connes and Marcoli have a very condensed yet readable "spark notes version" of QFT aimed at mathematicians. See especially their explanation of (Wick-rotated) Feynman integrals in elementary analysis.

  • This book by by Costello and Gwilliam has what is perhaps the "state of the art" mathematical point of view on quantum field theory in terms of rigor and naturality (it involves higher algebra).

  • "PCT, Spin and Statistics, and All That" by R. Streater and A. Wightman on the references. Recommanended by a participant: "it is a must for a mathematical perspective on QFT."

  • Quantum Field Theory on Curved Spacetimes by Baer and Frededenhagen or shorter "gem" Aspects of Quantum Field Theory in Curved Spacetime by Fulling for geometry perspective (also recommended by participant).

  • A list of QFT suggested readings for mathematicians by Peter Woit.