Physics 331 -- Quantum Field Theory

Physics 331 is the second course of Stanford's 3-quarter sequence on Quantum Field Theory. In the Winter Quarter 2020, this course is being given by Michael Peskin. The course meets on MW 11:30 - 12:50 in Hewlett 102.

General Course Information for Physics 331

Quantum Field Theory is at the same time the relativistic generalization of quantum theory and the foundation of the theory of elementary particles. It is a basic prerequisite for particle physics, string theory, condensed matter theory, and modern astrophysics and cosmology.

Physics 331 covers the following topics: functional integral formulation of quantum field theory, the infinities of quantum electrodynamics (and how to come to terms with them), the formulation and quantization of non-Abelian gauge theories, quantum chromodynamics, spontaneous symmetry breaking in theories with global and gauge symmetries, the Glashow-Salam-Weinberg model of weak interactions

The textbook for the course is An Introduction to Quantum Field Theory, by Peskin and Schroeder. The lectures will follow the text closely; relevant sections are indicated below. Other useful references are listed at the bottom of this page.

Here is the approximate syllabus for Physics 331, lecture by lecture: Lecture topics may be adjusted as the quarter proceeds.

Jan. 6 : Functional integral formulation of quantum mechanics and scalar field theory (P&S 9.1-3).
Jan. 8 : Functional integral formulation of spin 1/2 and spin 1 field theories (P&S 9.4-5)
Jan. 13 : Relation between the functional and the Hamiltonian formalism for correlation functions (P&S 4.2-4, 9.2, 9.6).
Jan. 15 : Kallen-Lehman representation, LSZ, and the Ward Identity (P&S 7.1-5)
Jan. 22 : 1-loop diagrams of QED (P&S 7.1, 6.3)
Jan. 27 : The QED vertex function (P&S 6.3-4)
Jan. 29: Vacuum polarization (P&S 7.5)
Feb. 3 : Infrared divergences of QED (P&S 6.4-5)
Feb. 5 : Non-Abelian gauge theories (P&S 15.1-3)
Feb. 10 : Quantization of non-Abelian gauge theories (P&S 16.1-2)
Feb. 12 : Asymptotic freedom (P&S 16.6)
Feb. 19 : Gauge theories at strong coupling
Feb. 24 : Quantum Chromodynamics (P&S 17.1-4)
Feb. 26 : The Altarelli-Parisi equations (P&S 17.5-6)
Mar. 2 : Quantum field theories with spontaneous symmetry breaking (P&S 11.1-2)
Mar. 4 : The Higgs mechanism (P&S 20.1)
Mar. 9 : The GSW theory of weak interactions (P&S 20.2-3)
Mar. 11 : Weak interactions at high energy (P&S 21.2-3)

This is not a course in particle physics. However, the Standard Model of particle physics and theoretical quantum field theory grew up in parallel, and it is a great help in learning each to study the other. To repair your education in particle physics, please take the course Physics 252 in the Spring Term. (Unfortunately, it is not given in Spring 2020.) A useful introduction to particle physics can also be found from my new book, Concepts of Elementary Particle Physics and from many of the books included below in the recommended reading.

Quantum field theory also has strong connections to statistical mechanics. These are discussed especially in Chapters 11-13 of Peskin and Schroeder's text. That material will be covered in Physics 332 in the Spring term.

Problem sets for Physics 331:

Problem Set 1 (due Jan. 15); solutions.
Problem Set 2 (due Jan. 22); solutions.
Problem Set 3 (due Jan. 29); solutions.
Problem Set 4 (due Feb. 5); solutions.
Problem Set 5 (due Feb. 12); solutions.
Problem Set 6 (due Feb. 19); solutions.
Problem Set 7 (due Feb. 26); solutions.
Problem Set 8 (due Mar. 4); solutions.
Problem Set 9 (due Mar. 11); solutions.

Exam for Physics 331: The final is available here. (with some corrections from the original version).

Final Exam; solutions.

Here are some final exams from my 331 courses in previous years: (Note that the syllabus was somewhat different each year.)