Phys 232A: Quantum Field Theory I

Fall 2013

shortcut to the homework assignments

Basic Info

Lecturer: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte.
GSI: Kevin Grosvenor (email: kgrosven@berkeley.edu)
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);

and

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.)

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.)

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 pdf file.

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 (page 181).

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 Keldysh-Schwinger formalism.

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, 2011)
E.A. Calzetta and B.-L. Hu, Nonequilibrium Quantum Field Theory (Cambridge, 2008)
J. Rammer, Quantum Field theory of Non-equilibrium States (Cambridge, 2007).

horava@berkeley.edu