Physics 232B: Quantum Field Theory II

Spring 2009

shortcut to the homework assignments

Basic Info

Time: Tue and Thu, 11:10am-12:30pm (lectures); Thu 5-6pm (discussion sessions)
Place: 402 Le Conte Hall

Instructor: Petr Hořava (email:
Offices - campus: 401 Le Conte Hall; LBNL: 50A-5107.
Office hours for 232B: Thu 3-4pm, 401 Le Conte.

This course is designed as a logical continuation of the introductory 232A. The emphasis will be on three main topics:

(i) path integrals methods in perturbative and nonperturbative QFT,
(ii) renormalization and the renormalization group concepts, and
(iii) quantization of non-Abelian gauge theories.

The main idea is to keep some balance between the techniques of and conceptual insights into QFT, stressing the universality of its applications not only in relativistic high-energy particle physics, but also in condensed matter theory, string theory, and even pure mathematics.

We will mainly use two primary textbooks:

A. Zee, Quantum Field Theory in a Nutshell (Princeton, 2003)


T. Banks, Modern Quantum Field Theory (Cambridge, 2008),

with occasional detours using Weinberg, Peskin-Schroeder, or review articles from the arXiv.

Since last year, Physics 232B replaced the previously taught Physics 230A. In order to see what this year's 232B might be like, you can look at the websites of my previous courses, 230A in Spring 2005 and 230A in Spring 2006. This year, the main novelty will be the existence of a new, very elegant and concise textbook by Banks, which we will use in conjuction with the book by Zee.

Homework Assignments

Homework assignments will be posted on this website weekly (or sometimes biweekly), on Thursdays before 2pm. Unless stated otherwise, the assignments will be due in one week's time, on Thursday in class. The solutions to the problems will be discussed in the first discussion session after the assignment is due. Most homeworks will be assigned from Zee's book, and I will refer to them by their number in Zee.

HW1 (due Thu, Jan 29): Problems I.2.1 and I.2.2 (on page 15 of [Zee]). In addition, one problem which is not from Zee's book is here as a pdf file.

HW2 (due Thu, Feb 5): Problems I.3.1, I.3.2 and I.4.1.

HW3 (due Thu, Feb 12): Problem I.5.1 from Zee; in addition, we will recycle two problems from 2006, namely problems (2) and (3) as given in this pdf file.

HW4 (due Thu, Feb 19): There is a total of five problems this week.
Problem (i): Look at Figure I.7.2, and draw all the missing Feynman diagrams that contribute at the given order in J and lambda.
Problem (ii): Same assignment, for Figure I.7.3. (The solutions to Problems (i) and (ii) can be found in the Errata to [Zee], but it is a good exercise to do without looking at the answer.)
In addition, Problems I.7.2, I.8.1, and I.8.4.

HW5 (due Thu, Feb 26): Problems I.9.1, I.9.3, I.10.2, and IV.1.1.

HW6 (due Thu, March 5): Problems II.1.1, II.1.2, II.1.11, II.3.4, and II.4.1.

HW7 (due Thu, March 12): Problems II.7.1, IV.7.1, and IV.7.4.

HW8 (due Thu, March 19): Problems III.3.1, III.3.2, III.3.3, III.3.4.
In addition, read pages 337-340 of Zee and solve problem VI.8.1, expressing the result not as a function of t but as a function of the RG scale mu.

HW9 (due Thu, April 2): Problems IV.3.1, IV.3.2, IV.3.3 and IV.3.4.

HW10 (due Thu, April 9): Problems IV.5.2, IV.5.3, IV.5.4. In addition, Problems 8.1 and 8.2 on page 132 of Banks's book. Before attacking these two problems, it will be useful to read Section 8.2 of [Banks] first; his notation for various fields of the BRST formalism differs significantly from the notation we used in class. More importantly, there is a typo in the assignment of Problem 8.2 -- the gauge-fixing Lagrangian should be an anticommutator of the BRST charge with a gauge-fixing fermion which is linear in the ANTIghost, not the ghost -- in other words, the "c" in his expression for the Lagrangian should have a bar on it.
HW11 (due in THREE WEEKS, on Thu, April 30): Problems VII.4.1, VII.4.4, VII.4.6, VII.1.2, VII.1.4, VI.8.3 and VI.8.4. This assignment represents our final homework assignment of the semester.