Phys 232A: Quantum Field Theory I

Fall 2018

shortcut to Homework Assignments

Basic Info

Discussion sessions:
Time: Tue and Thu, 2-3pm.
Place: 402 Le Conte Hall.
(The exact time and location of the Discussions may still be tweaked a bit, we are tring to optimize the timing so that the largest possible number of students can participate regularly in our Discussions.)

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: 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, 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, 234B and 233A in Spring 2019, and those courses will cover miscellaneous advanced material, including -- but not limited to -- 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, September 6): Read Appendix 2 of Chapter I.2 of [Zee] (which you will find on pages 14-16 of the 2nd edition). Solve Problem I.2.2 from [Zee] (on p. 16).

HW2 (due on Thursday, September 13): Problem I.2.1 from [Zee] (on p. 16). Problem I.3.1 from [Zee] (p. 24).

HW3 (due on Thursday, September 20): Problems I.3.2 (on p. 24) and I.4.1 (p. 31) from [Zee], and Problems 2.1(a,b) and 2.2(a) from [PS] (pp. 33-4).

HW4 (due on Thursday, September 27): Problem I.5.1 (on p. 39) from [Zee], Problem 2.2(b,c,d) from [PS] (p. 34).

HW5 (due on Thursday, October 4): Problems II.1.1, II.1.3, II.1.4, II.1.5 and II.1.11 (on pp. 105-6) from [Zee].

HW6 (due on Thursday, October 11): Problems II.2.1 and II.4.1 from [Zee] (on p. 113 and 122), Problem 3.4(a,b,c) from [PS] (on pp. 73-4).

HW7 (due on Thursday, October 18): Problems I.7.1, I.7.2 and I.7.3 from [Zee] (on p. 60).

HW8 (due on Thursday, October 25): Problems 4.1(a,b,c) and 4.3(a,b) from [PS] (pp. 126-8), and Problem II.6.7 from [Zee] (p.143) (this last problem is essentially equivalent to Problem 4.2 of [PS]).

HW9 (due on Thursday, November 1): Problems 4.3(c) and 4.4(a,b,c) from [PS] (pp. 128-130).

HW10 (due on Thursday, November 8): Problems II.5.2 (p. 131), III.1.2, III.1.3 (p. 168), III.2.1 (p. 172), III.3.1 and III.3.2 (p. 181); in addition, read as much of Chapter VI.8 as you can, and solve Problem VI.8.1 (p. 368), all from [Zee].

HW11 (due on Thursday, November 15): Problems III.3.3 and III.3.4 from [Zee] (p. 181), Problems 5.1 and 5.2 from [PS] (pp. 169-70).

HW12 (due IN TWO WEEKS, on Thursday, November 29): Problem III.6.1 on p. 198 of [Zee] (equivalent to Problem 3.2 of [PS]), and Problems 6.1 and 6.3(a,b) from [PS] (pp. 208-210). (In relation to Problem 6.1, see also the discussion in Problem III.6.4 on p. 199 in [Zee].)

Optional HW13: HW12 was our final official homework set this semester. I am happy to report that all students who turned in most of their homeworks have satisfied the criteria expected from this course, and all those students are therefore exempt from the final exam. There will still be lectures and discussion sessions during review week, as previously announced. As an optional homework set, I encourage you to look at the following problems: IV.3.3, IV.3.4 and IV.3.5 from [Zee] (p. 244). The solutions will be presented by Stephen (and discussed further) in our discussion sessions during review week.

horava@berkeley.edu