Introduction to Quantum Field Theory

The Introduction to Quantum Field Theory is a two-semester course. Content-wise, this is a continious 29-week long course, but for administrative purposes it is split in two:

Physics-wise, the split is rather arbitrary, so students seriously interested in the Quantum Field Theory should take both halves of the course.

Unfortunately, the UT Physics Department is unable to offer the QFT II class every year, so the students who take QFT I (396 K) this Fall (2011) will have to wait for the Spring of 2013 for the QFT II (396 L) course.

This document is the syllabus for the whole course as taught in the academic years 2011/12/13 (i.e., 396K taught in Fall 2011 and again in Fall 2012, and 396L taught in Spring 2013) by Dr. Vadim Kaplunovsky. Note that future offering of the Quantum Field Theory course may vary.

Prerequisite Knowledge

Understanding Quantum Field Theory requires serious knowledge of quantum mechanics at graduate or advanced undergraduate level. Knowing how to solve the hydrogen atom is not enough — a student must be familiar with multi-oscillator systems, spin, identical particles, perturbation theory, and scattering. Besides QM, undergraduate-level knowledge of classical mechanics, E&M, and statistical mechanics would also be very useful.

The formal prerequisite for the 396 K class is 389 K (Graduate Quantum Mechanics I), but the real prerequisite is the knowledge rather than the grade. If you have already taken a graduate-level QM course elsewhere, or took two undergraduate semesters (80+ hours) of QM (not counting an introductory Modern Physics class or applied QM classes such as Atoms and Molecules) — or if you have learned enough QM by yourself — I shall waive the prerequisite. But if your QM knowledge stops with the single-electron wave-function and the hydrogen atom but J. J. Sakurai's Modern Quantum Mechanics is all Japanese to you, then taking my QFT class right away would be rather unwise and you should really take the 389K course first.

Course Content (QFT I and QFT II combined)

Bosonic Fields:
Classical field theory; relativistic fields; identical bosons and quantum fields; Klein-Gordon propagator and relativistic causality; quantum electromagnetic fields and photons.
Fermionic fields:
Lorentz symmetry and spinor fields; Dirac equation and its solutions; second quantization of fermions and particle-hole formalism; quantum Dirac field; Weyl and Majorana spinor fields.
Symmetries in QFT:
Continuous symmetries and conserved currents; spontaneous symmetry breaking and Goldstone bosons; local (gauge) symmetry and QED; Higgs mechanism and superconductivity; non-abelian gauge symmetries and the Yang-Mills theory; discrete symmetries.
Interacting Fields and Feynman Rules:
Perturbation theory; correlation functions and Feynman diagrams; S-matrix and cross-sections; Feynman rules for fermions; Feynman rules for QED.
Quantum Electrodynamics:
Some elementary processes; radiative corrections; infrared and ultraviolet divergencies; renormalization of fields and of the electric charge; Ward identities.
Functional Methods:
Path integrals in quantum mechanics; "path" integrals for classical fields and functional quantization; functional quantization of QED; QFT and statistical mechanics; quantum symmetries and conservation laws.
Renormalization Theory:
Systematics of renormalization; `integration out' and the Wilsonian renormalization; `running' of the coupling constants and the renormalization group.
Non-Abelian Gauge Theories:
Non-abelian gauge symmetries and the Yang-Mills theory; interactions of gauge bosons and Feynman rules; Fadde'ev-Popov ghosts and BRST; renormalization of the YM theories and the asymptotic freedom; chiral gauge symmetries; the Standard Model; confinement and other non-perturbative effects.

In the first semester (the 396 K course) I shall cover the bosonic and the fermionic fields, the symmetries (including the Higgs mechanism and the non-abelian gauge symmetries at the semi-classical level), the perturbation theory and the Feynman graphs, and the elementary processes in QED. The remaining subjects will be covered in the second semester (the 396 L course).


The primary textbook for this course (both semesters) is An Introduction to Quantum Field Theory by Michael Peskin and Daniel Schroeder. To a large extent, the course is based on this book and should follow it fairly closely, but don't expect a 100% match.

Since both the course and the main textbook are introductory in nature, many questions would be left an-answered. The best reference book for finding the answers is The Quantum Theory of Fields by Steven Weinberg. The first two volumes of this three-volume series are based on a two-year course Dr. Weinberg used to teach here at UT — but of course they also contains much additional material. To a first approximation, Dr. Weinberg's book teaches you everything you ever wanted to know about QFT and more — which is unfortunately way too much for a one-year intoductory course. (Weinberg's volume 3 is about supersymmetry, a fascinating subject I would not be able to cover at all in this course.)

I have told the campus bookstore that I use Peskin's book as a textbook for both 396 K and 396 L (Fall 2011, Fall 2012, and Spring 2013), Weinberg's vol.1 as a supplementary texbook for the 396 K (Fall 2011 and Fall 2012) and vol.2 as a supplementary textbook for the 396 L (Spring 2013). I hope the store have stocked the books accordingly, but you should buy them while the supply lasts.

Homeworks and Grades

The homeworks are absolutely essential for understanding the course material. Often, due to the time pressure, I will explain the general theory in class and leave the examples for the homework assignment. t is extremely important for you to work them out by yourselves; otherwise, you might think you understand the class material but you would not! Be warned: The homeworks will be very hard.

I shall post homework assignments each week on page The solutions will be linked to the same page after the due date of each assignment.

The homeworks are assigned on the honor system: I shall not collect or grade the homeworks, but you should endeavor to finish them on time and check each other's solutions.

The solutions to previous years' homeworks — often quite similar to this year's — are available on the web, even on my own web server. On the honor system, I will keep them available at all times. But you should do your best to do the homework yourself, and only then read the solutions I post.

There will be separate final grades for each semester. Each grade is based on two take-home tests, one in the middle of the semester, the other at the end; the mid-term test contributes half of the grade and the end-term test the other half. There will be no in-class final exams.

Logistics (Fall 2011 semester)

Regular Lectures

Make-up and Supplementary Lectures

The supplementary lectures will cover issues that are somewhat ouside the main focus of the course but are interesting for their own sake, such as conformal symmetry or superconductivity. The students are strongly encoraged to attend the supplementary lectures, but there is no penalty for missing them. The issues covered by supplementary lectures will not be necessary to understand the regular lectures and will not appear on exams.


Last Modified: November 22, 2011.
Vadim Kaplunovsky