Phys 232A: Quantum Field Theory I

Fall 2012

Basic Info

Time: Lectures on Tue and Thu, 9:40-11:00am.
Discussion sessions: Fridays 3:10-4pm.
Place: 402 Le Conte Hall.

Lecturer: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte.
Office hours: Wednesdays 11am-12noon.
GSI: Kevin Grosvenor (email: kgrosven@berkeley.edu)
GSI office: 420K Le Conte.
GSI office hours: Tuesdays 2pm, Wednesdays 1pm.

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.)

Prerequisites

Graduate-level quantum mechanics. Basics of special relativity.

Homeworks and Grading Policy

There will be weekly homework assignments, posted on this website. Now that we know that the course does have a GSI, I can finally say that the style of homework grading will be entirely up to our GSI :-)

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.)

Homework Assignments

The homework assignments will be posted here weekly, on Thurdays around noon, and will be due in class on Thursday, one week later. Most HWs will refer to specific problems in Zee ([Zee]) or Peskin-Schroeder ([PS]). Solutions will then be discussed in the Friday discussion session (unless stated otherwise by the GSI).

HW1 (due on Thu, Sept. 6): Problems I.2.1 and I.2.2 from [Zee] page 16 (of the 2nd edition; note that the page numbers between 1st and 2nd addition changed! These same problems in 1st edition are on page 15. From now on, all HW references to problems from [Zee] will refer to the page numbers in the 2nd edition); and Problem 2.1(a) from [PS] (page 33).

HW2 (due on Thu, Sept. 13): Problems 2.1(b) and 2.2 of [PS] (pages 33-34).

HW3 (due on Thu, Sept. 20): Problems 3.1, 3.2 and 3.5 of [PS] (pages 71-75).

HW4 (due on Thu, Sept. 27): Problems I.3.3 (pages 24-25) and I.4.1 (p.31) of [Zee], and Problem 3.4 of [PS] (pages 73-74).

HW5 (due on Thu, Oct. 4): Problems I.7.1, I.7.2 and I.7.3 from [Zee] (page 60).

HW6 (due on Thu, Oct. 11): Problems 4.2 and 4.3 from [PS] (pages 127-128).

HW7 (due on Thu, Oct. 18): Problem 4.4 from [PS] (pages 129-130), Problem I.5.1 from [Zee] (p. 39).

HW8 (due on Thu, Oct. 25): Problem 5.3 (a,b,c,d) from [PS] (pages 170-171), Problems III.1.1 and III.1.3 from [Zee] (p. 168).

HW9 (due on Thu, Nov. 1): This week's problems are all from [Zee]: III.3.1, III.3.2 and III.3.3 (p. 181), and III.6.3 (p. 198).

HW10 (due on Thu, Nov. 8): Problem 6.3 (a,b) from [PS] (page 210), Problem IV.3.4 from [Zee] (p. 244).

HW11 (due on Thu, Nov. 15): Problem 11.3 from [PS] (pages 390-391).

HW12 (due IN TWO WEEKS, on Thu, Nov. 29): Problem 7.3 from [PS] (pages 257-8) and Problem IV.7.4 from [Zee] (page 279).

HW12 is the last HW assignment of this course.

horava@berkeley.edu