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, soThis document is the syllabus for the whole course as taught in the academic year 2004/05 (*i.e.*, **396K** taught in Fall 2004, and **396L** taught in Spring 2005) by **Dr. Vadim Kaplunovsky**. Note that future offering of the Quantum Field Theory course may vary.

Understanding Quantum Field Theory requires graduate 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 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 learned it yourself -- I shall agree to waive the prerequisite; it's the knowledge that's required, not the grade. But if you have only taken a regular underground-level 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.

- Bosonic Fields:
- Second quantization of bosons; non-relativistic quantum fields and the Landau Ginzburg theory; relativistic free particles and the Klein-Gordon field; causality and the Klein-Gordon propagator; quantum electromagnetic fields and photons.
- Fermionic Fields:
- Second quantization of fermions; particle-hole formalism; Dirac equation and its non-relativistic limit; quantum Dirac field; spin-statistics theorem; Dirac matrix techniques; Lorentz and discrete symmetries.
- Interacting Fields and Feynman Rules:
- Perturbation theory; correlation functions; Feynman diagrams; S-matrix and cross-sections; Feynman rules for fermions; Feynman rules for QED.
- 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.
- Quantum Electrodynamics:
- Some elementary processes; radiative corrections; infrared and ultraviolet divergencies; renormalization of fields and of the electric charge; Ward identity.
- 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.

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 thus 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 than some 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 semesters, Weinberg's vol.1 as a supplementary texbook for the Fall semester and vol.2 as a supplementary textbook for the Spring. I hope the store have stocked the books accordingly, but you should buy them while the supply lasts.

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. 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. Eventually, I shall post the homework solutions on the web, but 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.

Virtual hours are for administrivia and

Last Modified: August 24, 2004. Vadim Kaplunovsky

vadim@physics.utexas.edu