Quantum field theory (QFT) is the deepest physical theory we have. Much of modern physics is really QFT, and most of the physics news you see is about QFT: string theory, the Higgs boson, particle colliders, glueballs, etc.
Unfortunately, most people (even most physicists) will not learn QFT. The point of this website is to help people learn QFT. You learn physics by doing physics (solving problems), and most people trying to learn QFT run into two roadblocks: selecting a representative and finite set of problems and having good solutions to consult when they get stuck. I have solved both problems by uploading the homework assignments and exams, along with full solutions, for the QFT sequence at the University of Michigan (Physics 513 and 523).
I have also uploaded my personal notes. These help explain my notation and show how to calculate symmetry factors for loop diagrams. They also contain more worked-out problems.
There is a lot of material here, and certainly there are mistakes. If you find any in the homework or exam solutions, please let me know. I don't want to know about mistakes in the notes. Good luck.
To learn QFT, you need a solid understanding of undergraduate physics and graduate-level nonrelativistic quantum mechanics. The latter is covered in Sakurai & Napolitano’s Modern Quantum Mechanics.
I think you should learn general relativity (GR) before QFT. GR and QFT represent major jumps compared with the rest of physics, and many QFT ideas are first encountered in GR in a simpler form, including classical field theory and tensors. Sean Carroll’s Spacetime and Geometry: An Introduction to General Relativity is excellent. QFT assumes special relativity (SR), so at the very least, if you don’t want to learn GR first, you need to understand SR (Chapter 1 of Carroll’s textbook). I adopt most of Carroll’s SR notation.
You are going to need a textbook. I recommend Matthew D. Schwartz’s Quantum Field Theory and the Standard Model. This is the textbook I used and the material in these solutions corresponds to the first 26 chapters of Schwartz. Most of my QFT notation comes from Schwartz (though I deviate from him in several places).
For other fields of physics there are standard textbooks that cover everything you need in a self-contained, well-organized form. Usually there are several such books. David J. Griffiths’s Introduction to Electrodynamics is a classic example. Unfortunately, there is nothing like that for QFT. QFT is the cutting edge of physics and is too messy and large to be condensed to one textbook. No textbook is going to be the silver bullet that has everything you need. Some textbooks are better for different things, and you’ll probably have to get at least two.
Lastly, I strongly recommend Sean Carroll’s Quanta and Fields: The Biggest Ideas in the Universe. This is not a textbook. It is a popular book that tells you how to interpret QFT. Textbooks are too focused on solving problems and usually leave this part out. But these qualitative explanations help you understand the math better.
Pavel Okun, PhD (pokun@umich.edu)