Physics 232B: Quantum Field Theory II
shortcut to the homework assignments
Time: Tue and Thu, 11:10am-12:30pm (lectures);
Thu 5-6pm (discussion sessions)
Place: 402 Le Conte Hall
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
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 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
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
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,
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,
HW8 (due Thu, March 19): Problems III.3.1, III.3.2,
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.