Physics 230A - Quantum Field Theory I

Basic Info

Spring 2005, Tue and Thu, 9:30 - 11:00 a.m., 430 Birge Hall
Discussions: Fri, 2:10 - 3:00 p.m. (originally in 385 Le Conte Hall; effective immediately, relocated to the Oppenheimer Room, 4th floor Birge)
(Sometimes, by announcement, the discussion will be moved to Thu, 4:10 p.m., Oppenheimer room.)

Instructor: Petr Hořava (email:
Office: 441 Birge (usually on Tue and Thu); 50A-5107 LBNL (usually on Mon, Wed, Fri)

Homework Assignments

Homework assignments will be posted here every Thursday by noon (or later :-), and they will be due in class in seven days. They will be graded on a crude scale, + or - (+ for reasonable effort, - for not turning the homework in or for no visible effort). Unless stated otherwise, the problems are from A. Zee's book.

Week 1: No official homework; instead, an Opening Quiz has been handed out.
Week 2: Problems I.3.1, I.3.2, I.4.1, I.5.1 (due Thu, Feb 3).
Week 3: Problems I.7.1, I.7.2, I.7.3, I.7.4, I.8.1, I.8.3, I.8.5 (due Thu, Feb 10).
Week 4: Problems I.9.1, I.9.3, I.9.4, I.10.2, I.10.3, I.10.4 (due Thu, Feb 17).
Week 5: Problems II.1.1, II.1.2, II.1.3, II.1.8, II.1.11, II.2.1, II.4.1 (due Thu, Feb 24).
Week 6: From the perspective of Zee's book, this week we were hopping around and effectively sampling different chapters. As a result, the homework problems are from several different parts of the book. Here they are: II.3.2, II.3.4, II.5.1, III.5.1, III.5.2, V.5.1 (due Thu, March 3).
Week 7: Just two problems: V.6.1, V.6.2 (due Thu, March 10).
Week 8: Problems IV.1.2, IV.4.3, IV.4.4, IV.5.1, IV.5.2, IV.5.4 (due Thu, March 17).
Week 9: This week's problems can be found here. In addition to the three problems there, you are also required to read Chapter IV.6 of Zee (on the Higgs mechanism). The three problems are due Thu, March 31. Any questions about the Higgs mechanism will be addressed in discussion in April.
Week 10: Spring break.
Week 11: This week's discussion (on April 1) has been cancelled, and there is no homework this week. Next week's discussion will be held on Thu, April 7, 4:10pm in the Oppenheimer room; there is no discussion on Fri, April 8.
Week 12: Problems VI.1.1, VI.1.2, VI.1.4, VI.6.2, VI.6.3, VII.1.1, VII.1.4 (due Thu, April 14).
Week 13: Problems VI.1.7, VI.7.1, VI.8.3, VII.4.1, VII.4.4 (this problem is related to the material to be covered in class on Tue, April 19) -- (due Thu, April 21).
Week 14: Problems VII.4.5 and VII.4.6 (due Thu, April 28); in addition, as a part of this week's assignment, read as much as you can of J. Maldacena's TASI 2003 lectures on the AdS/CFT correspondence, hep-th/0309246; our discussion session on Fri, April 29 will be (primarily) on AdS/CFT.
Week 15: Problems IV.3.3, IV.3.4, III.1.3, III.3.1, III.3.2, III.3.4. This is the final official homework assignment of the semester (due Thu, May 5).

Week 16: I was originally planning to post an official final take-home exam here. However, I have decided that there will be no official take-home exam. I am happy with how hard the students have worked throughout the semester, on all those homework assignments. I feel that I have enough information to assign grades solely on the homework performance (plus the students' activity in class and in discussions). At this point, the spectrum of grades will range from the best grade of A+, to the worst grade of A-. If somebody feels that they might fall into the A- category and are unhappy about it, they can still convince me that they deserve an A+, by solving the otherwise voluntary problem below. (If you intend to do so, please let me know by May 11.)
So, instead of a mandatory final exam, I offer the following problem, to those who wish to test their understanding of the material of the course:

    Voluntary problem. We all know that in four spacetime dimensions, the coupling constant of the scalar field theory with the (phi)^4 self-interaction runs, and the theory is driven to strong coupling at large energies. Consider now the scalar field theory in 5+1 spacetime dimensions, with the (phi)^3 self-interaction. Show -- in the lowest order in the perturbation theory in the small coupling constant -- that the coupling constant of this (phi)^3 theory also runs, but the theory is now asymptotically free. [Hint: This is not as simple as it may sound -- you have to take into account the wave-function renormalization of the scalar field.]
One final piece of information: Those of you who would like to further practice their understanding of the material covered in class during Week 16 could consider problems IV.7.1, IV.7.4, III.7.1, VI.8.1 and VI.8.7 (this somewhat tersely defined problem is explained in more detail in the body of the chapter, and in the solutions at the end of the book).
Week 17: Our final class is scheduled for Tue, May 10, 9:40-11am, in 430 Birge as usual. For the rest of the week of May 9-13, I recommend that you attend as many talks of our math/physics workshop on matrix models as you can. Thanks for a great semester, I really enjoyed it! I hope to see you in the Fall semester in my Phys-250 class on AdS/CFT correspondence!

The course is designed as a logical continuation of the material covered in 229A, with three major themes: the path integral method, renormalization in quantum field theory, and quantization of Yang-Mills theories. My intention is to keep some balance between the techniques of and conceptual insight into (both perturbative and non-perturbative) quantum field theory in general.

In this course, we will primarily use two textbooks:

A. Zee, Quantum Field Theory in a Nutshell


M.E. Peskin & D.V. Schroeder, An Introduction to Quantum Field Theory.