Phys 232A: Quantum Field Theory I

Fall 2017

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Basic Info

Discussion sessions:
Time: Tuesdays 2:10-3pm, Fridays 11:10am-12noon.
Place: 402 Le Conte Hall.

Lecturer: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte Hall.
Office hours: Thursdays 1-2pm.

GSI: Stephen Randall.
Office: 420B Le Conte Hall.
Office hours: Mondays 11am-12noon.

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, statistical mechanics, 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).

I also strongly recommend

M.D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge, 2014).

There are now many many more texts on QFT, some excellent, some not so much. We will try to focus on the first two listed above, while adding some additional material of interest at least occasionally, from Zee and other sources. (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 rough plan for what will be covered in this semester: [Peskin & Schroeder] (or [PS] for short) consists of Parts I, II and III. We will NOT cover anything from Part III (which deals mostly with Yang-Mills and the Standard Model), but will cover Part I, and a big portion of Part II. Luckily, there is also 232B in Spring 2018, in which we will expand into miscellaneous advanced and fun -- often interdisciplinary -- directions, not limited to just portions of Part III of [PS].

The final grade will 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 was explained 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 discussion sessions and lectures, you will be exempt from the final exam. (Other permutations work as well.)

HW1 (due on Thursday, Sept 7): Problems I.2.1 and I.2.2 from [Zee] (they are on page 16 of the 2nd edition).

HW2 (due on Thursday, Sept 14): Problems 2.1(a), 2.1(b) and 2.2(a) from Peskin&Schroeder [PS] (on pp. 33-34).

HW3 (due on Thursday, Sept 21): Problems I.3.1, I.3.3 and I.4.1 from [Zee] (on pages 24-5,31).

HW4 (due on Thursday, Sept 28): Problem 2.2(b,c) from [PS] (on page 34) and Problems I.5.1, I.8.1 and I.8.2 from [Zee] (pages 39, 69).

HW5 (due on Thursday, Oct 5): Problem 3.1(a,b,c) from [PS] (on pages71-2). Read Appendix E of [Zee] and solve Problem E.1 (on p. 544 of [Zee]); treat the spinors as anticommuting, Grassmannian variables!

HW6 (due on Thursday, Oct 12): Read Chapter 3.6 of [PS] which deals with the discrete symmetries of the Dirac fermions, and solve Problem 3.7(a) of [PS] (p. 75). In addition, solve the following problems from [Zee]: II.1.7 (on p. 105), II.1.11 and II.1.12 (p. 106), II.2.1 (p. 113).

HW7 (due on Thursday, Oct 19): Problems I.7.1, I.7.2, I.7.3 and I.7.4 from [Zee] (on p. 60).

HW8 (due on Thursday, Oct 26): Problem 4.3(a), 4.3(b) of [PS] (pp. 127-8) In part (a) of that problem, do NOT calculate the differential cross-section (yet). Problems III.1.1 and III.1.3 from [Zee] (on page 168).

HW9 (due on Thursday, Nov 2): Today's problems are all from [PS], on pages 128-130: First, complete the rest of Problem 4.3(a), i.e., calculate the differential cross-section; then solve Problem 4.3(c), and all parts (a), (b) and (c) of Problem 4.4 (Rutherford scattering). I leave 4.3(d) as optional, we will not return to it later, but it is a nice and illuminating extension of what you've already learned in 4.3(a-c).

HW10 (due on Thursday, Nov 9): Chapter 5 of [PS] deals with tree-level calculations of various physical processes in QED. You now have all the conceptual ingredients for calculating these processes. Read as much of the Chapter as you find practical, and solve Problems 5.1 and 5.2, which appear on pages 169-70 of [PS]; in Problem 5.1, you don't have to rederive the Mott formula in the second way suggested in [PS], but you are certainly welcome to do so. In addition, solve a small easy problem from [Zee]: III.3.2 (on page 181).

HW11 (due on Thursday, Nov 16): Two of the problems for this week appear both in [PS] and in [Zee]: First, Problem 3.2 of [PS] (on p.72), essentially equivalent to Problem III.6.1 of [Zee] (p. 198). The second one is Problem 6.1 of [PS] (p. 208), which shares a lot with Problem III.6.4 of [Zee] (p.199). In addition, Problem III.6.2 of [Zee] (p. 198) provides another check of what we argued to be true in class.

HW12 (due IN TWO WEEKS, on Thursday, Nov 30): Problem 6.3(a) from [PS] (on page 210), Problems IV.3.3, IV.3.4 and IV.3.5 from [Zee] (on page 244), Problem 11.3(a,b,c,d,e) from [PS] (page 390-1).

HW13 (this homework is NOT mandatory; it is due on Thursday, Dec 7): All Problems are from [Zee]: VI.6.1 (page 349), VI.8.3 and VI.8.4 (page 368), V.2.1 and V.2.2 (page 291).

All grading has been completed, and I am very happy to announce officially that everyone has been exempt from the final exam. This means that everyone has earned either an A or an A+! Thank you all for your hard work, the credit goes to all the students and to Stephen, our amazing GSI! :)

horava@berkeley.edu