Quantum Field Theory I

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:

In the academic year 1998/99, Dr. Vadim Kaplunovsky teaches both semesters of the Quantum Field Theory course. This document is the syllabus for the first semester, i.e., PHY 396K course (unique #56330) taught in the Fall of 1998. The second semester of the QFT course (PHY 396L taught in the Spring of 1999) is described in a separate syllabus.

Note that future offering of the Quantum Field Theory course may vary.

Course Content

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; optical theorem and other formal developments; Ward identity.

* I expect to begin teaching QED towards the end of the first semester and finish the subject in the second semester.

Textbooks

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. This two-volume book is based on a two-year course Dr. Weinberg used to teach here at UT -- but of course it also contains much additional material. To a first approximation, Weinbergs 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.

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.

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. 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; if you do not work them out by yourself, you would not really understand what I was talking about in class! Be warned: The homeworks will be very hard.

The grades will be based on two take-home test, one at the middle of the semester, the other at the end. Each test will account for 50% of the final grade. There will be no in-class final exam.

Logistics

Lectures

Office Hours