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:

  • PHY 396 K -- Quantum Field Theory I, usually taught in the Fall, and
  • PHY 396 L -- Quantum Field Theory II, usually taught in the Spring.
  • Physics-wise, the split is rather arbitrary, so the 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 (2007) will have to wait for the Spring of 2009 for the QFT II (396 L) course.

    This document is the syllabus for the whole course as taught in the academic years 2007/08/09 (i.e., 396K taught in Fall 2007 and again in Fall 2008, and 396L taught in Spring 2009) by Dr. Vadim Kaplunovsky. Note that future offering of the Quantum Field Theory course may vary.

    Required Knowledge

    Understanding Quantum Field Theory requires graduate-level (or at least advanced undergraduate level) knowledge of quantum mechanics. Knowledge of classical mechanics, E&M, and statistical mechanics is also very useful, but quantum mechanics is absolutely essential and the typical undergraduate-level QM just isn't enough.

    The formal prerequisite for the 396 K class is 389 K (Graduate Quantum Mechanics I). If you have already taken a graduate-level QM course elsewhere, or took two undergraduate semesters (80+ hours) of QM (not counting the introductory Modern Physics course or applied QM courses such as Atoms and Molecules). — or if you learned enough QM by yourself — I shall waive the prerequisite; it's the knowledge that's required, not the grade. But if you have only taken a one-semester undergraduate QM and J. J. Sakurai's Modern Quantum Mechanics is all Japanese to you, than taking the QFT course 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 free particles and the Klein-Gordon field; non-relativistic quantum fields and the Landau Ginzburg theory; symmetries and spontaneous symmetry breaking; causality and the Klein-Gordon propagator; 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; discrete symmetries; Weyl and Majorana spinor fields.
    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; 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; 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; the Standard Model.

    In the first semester (the 396 K course) I will cover the bosonic and the fermionic fields and related issues (see above), the perturbation theory and the Feynman graphs, the elementary processes in QED, and maybe a bit of non-abelian gauge theory. 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 2007, Fall 2008, and Spring 2009), Weinberg's vol.1 as a supplementary texbook for the 396 K (Fall 2007 and Fall 2008) and vol.2 as a supplementary textbook for the 396 L (Spring 2009). I hope the store have stocked the books accordingly, but you should buy them while the supply lasts.

    Homeworks and Grades

    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.

    I shall post the homework assignments on this web page. The solutions will be posted — after the due date — as PDF files linked to the same page.

    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.

    Note that 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. It 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.

    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.




  • Office Location: RLM 9.314A.
  • Reserved Office Hour: Wednesday, 3-4 PM.
  • Other Office Hours: Students are welcome whenever I'm in my office and not too busy. The best times to look for me are late afternoons and early evening hours, and also Thursday between the brown bag seminar and the class.
  • E-mail: Please send plain-text or HTML only, no MSWord attachments.
    Please use email for simple homework questions or administrivia. Complicated physics questions should be asked in person.

  • Last Modified: September 14, 2007.
    Vadim Kaplunovsky