Phys 232A: Quantum Field Theory I
shortcut to the homework assignments
Time: Lectures on Tue and Thu, 9:40-11:00am.
Discussion sessions: TBD.
Place: lectures: 402 Le Conte Hall (ideally, also discussions).
Office: 401 Le Conte.
GSI: Kevin Grosvenor
GSI office: 420K Le Conte.
GSI office hours: TBD.
Quantum field theory (QFT) and, more generally, many-body theory, represents
the leading paradigm in modern theoretical physics, and an absolutely
essential ingredient in our current understanding of the Universe on
an astonishingly diverse range of scales. The basic ideas and techniques
of QFT are at the core of our understanding of high-energy particle physics
and cosmology, as well as phenomena in condensed matter and even finance.
QFT also naturally leads to its logical extension -- string theory -- which
in turn provides a unified framework for reconciling the quantum paradigm
with the other leading paradigm of the 20th century physics: that of general
relativity, in wich gravity is understood as the geometry of spacetime.
At the core of the modern understanding of QFT is the so-called Wilsonian
framework: A way of understanding how interacting systems with many degrees
of freedom reorganize themselves as we change the scale at which we observe
the system. This makes concepts and techniques of QFT remarkably universal,
and applicable to just about every area of physics. As a result, a solid
understanding of the basic structure, ideas and techniques of QFT is
indispensable not only to high-energy particle theorists and experimentalists,
or condensed matter theorists, but also to string theorists, astrophysicists
and cosmologists, as well as an increasing number of mathematicians.
This course will provide the introduction to the principles of QFT, mostly in
-- but not limited to -- the special case of the relativistic regime. The
focus will be two-fold: First, on developing a "big-picture" understanding
of the basic ideas and concepts of QFT, and equally on developing the
techniques of QFT, including renormalization and the renormalization group.
The two main textbooks are going to be:
M.E. Peskin and D.V. Schroeder, An Introduction to Quantum
Field Theory (Perseus, 1995);
A. Zee, Quantum Field Theory in a Nutshell. 2nd edition
(Princeton U.P., 2010).
There are now many many more texts on QFT, some excellent, some not so much.
We will try to focus on the two listed above, while adding some additional
material of interest at least occasionally. (In the case of Tony Zee's book,
it is definitely worth buying the 2nd edition. It is substantially
expanded compared to the 1st; and notably, many many typos of the 1st edition
have also been corrected in the 2nd.)
Graduate-level quantum mechanics. Basics of special relativity.
Homeworks and Grading Policy
There will be weekly homework assignments, posted on this website. Since
our course does have a GSI, the style of homework grading will be entirely
up to him :-)
The final grade will then be based on three things: 1. homeworks, 2.
participation in discussions (during discussion sessions as well as lectures),
and 3. the final exam. As I have done with other classes in previous years,
I will again apply the "two-out-of-three" rule, which I will explain clearly
in class. Briefly, it means that for a good grade (say an A) it is sufficient
to do really well on two out of 1., 2. and 3. listed above; for example,
if you do great on homeworks and you interact well in discussions and homework
presentations in discussion sessions, you will be exempt from the final exam.
(Other permutations work as well.)
Starting from HW2, the homework assignments will be posted here weekly
on Tuesdays around noon, and will be due in class on Tuesday, one
week later. HW1 is an exception from this rule, as it is assigned
on a Thursday, and due also on Thursday. Most HWs will refer to specific
problems in Zee ([Zee]) or Peskin-Schroeder ([PS]). Solutions will then be
discussed in the discussion session (unless stated otherwise by the GSI).
HW1 (due on Thu, Sept. 12): Problems I.2.1 and I.2.2 from
[Zee], page 16 (of the 2nd edition; in the 1st edition the same problems are
on page 15).
HW2 (due on Tue, Sept. 17): Problems 2.1(a),(b) and 2.2(a)
from [PS] (on pages 33-4).
HW3 (due on Tue, Sept. 24): Problems 2.2(b),(c),(d)
from [PS] (on page 34), plus one problem in the following
HW4 (due on Tue, Oct. 1): Problems from [Zee]: I.4.1 (on
page 31), I.5.1 (on page 39) and I.8.1 (on page 69).
HW5 (due on Tue, Oct. 8): Problems from [PS]: 3.1(a,b,c)
and 3.4(a,b,c), on pages 71-74.
HW6 (due on Tue, Oct. 15): Problem I.7.2 from
[Zee], page 60; and Problem 4.3(a),(b) from [PS], pages 127-128.
HW7 (due on Tue, Oct. 22): Problems 4.1(a),(b),(c) and
4.4(a),(b),(c) of [PS] (pages 126-30).
HW8 (due on Tue, Oct. 29): Problems 5.1 and
5.3(a),(b),(c),(d) of [PS], pages 169-171.
HW9 (due on Tue, Nov. 5): Problems from [Zee]:
III.1.3 (page 168), III.2.1 (page 172), III.3.1, III.3.2, III.3.4 and III.3.5
HW10 (due on Tue, Nov. 12): Problems from [PS]:
6.1 (pp.208-9) and 6.3(a),(b) (p.210).
HW11 (due on Tue, Nov. 19): Problems from [Zee]:
IV.3.4 and IV.3.5 on page 244.
HW12 (due IN TWO WEEKS, on Tue, Dec. 3): This is the
last HW assignment of this course. It contains three problems, but for
full credit it is sufficient to do two (you can choose any two, out of
those three). Problem 7.3 from [PS] (pages 257-8); Problem IV.7.4 from [Zee]
(page 279); Problem III.8.1 from [Zee] (page 218).
The lecture on Tue, November 26 (the week of Thanksgiving), will be given
by Misha Smolkin, he will talk about his work using the
Here are some textbook references on the use of the Keldysh-Schwinger
formalism, as I promised in class.
(They are NOT required reading for Misha's lecture :)
A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge,
E.A. Calzetta and B.-L. Hu, Nonequilibrium Quantum Field Theory
J. Rammer, Quantum Field theory of Non-equilibrium States (Cambridge,