Phys 232A: Quantum Field Theory I

Fall 2014

shortcut to the homework assignments

Basic Info

Lecturer: Petr Hořava (email: horava@berkeley.edu)
Office: 401 Le Conte Hall.
GSI: Sean Jason Weinberg (email: sjweinberg@berkeley.edu)

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

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

I also strongly recommend

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 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.

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 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 Tue, Sept. 16): Problems I.2.1 and I.2.2 from [Zee]. These problems are on page 16 of the 2nd edition of the book. WARNING: In the rest of the semester, I will always refer to the page numbers of the 2nd edition of [Zee], always ignoring the 1st edition!

HW2 (due on Tue, Sept. 23): Problems 2.2.1(a,b) and 2.2.2(a) on pages 33-34 of Peskin-Schroeder ([PS] for short), plus one problem contained in this pdf file.

HW3 (due on Tue, Sept. 30): Problems I.3.1 (on p. 24) and I.4.1 (p. 31) from [Zee], and Problems 2.2.2(b,c,d) on p. 34 of [PS].

HW4 (due on Tue, Oct. 7): Problems 3.1(a) (on p. 71) from [PS], I.3.3 (p. 24) and I.5.1 (p. 39) from [Zee].

HW5 (due on Tue, Oct. 14): Problems 3.1(b,c), 3.2, 3.4(a,b,c) (on pp. 72-74) from [PS].

HW6 (due on Tue, Oct. 21): Problem 3.5 (on pp. 74-5) from [PS], Problem I.7.2 from [Zee, p. 60], Problem 4.3(a) from [PS, p.127-8]; please do only the first part of this problem (a), including the propagator and the vertex but excluding the cross-section calculation.

HW7 (due on Tue, Oct. 28): Problems 4.1(a,b,c) and 4.3(b,c) from [PS] (on pages 126-129). Apologies for the slight delay in the posting of this assignment.

HW8 (due on Tue, Nov. 4): Problem 4.4(a,b,c) from [PS] (on pages 129-30), and the part of 4.3(a) which deals with the differential cross-section and was left out in HW6.

HW9 (due IN NINE DAYS, on Thu, Nov. 13 -- no class on Tue, Nov 11: Veterans' Day): Problems 5.1 and 5.2 from [PS, pp.169-70], Problem III.1.3 from [Zee, p. 168], and Problem VI.8.2 (only the case of the lambda phi^4 theory) from [Zee, p. 368].

HW10 (due on Thu, Nov. 20): Problems III.2.1 [Zee, p. 172], III.3.1, III.3.2, III.3.4 and III.3.5 [Zee, p. 181].

HW11 (due on Tue, Dec. 2): Problems IV.3.3, IV.3.4 and IV.3.5 (on page 244 of [Zee]), Problem 6.3(a) (on page 210 of [PS]).

Now that the HW assignments have been completed, here is an update on the final grading: Most students have already qualified for an A, based on my "2-our-of-3" rule, and are therefore exempt from the final exam. Those few who will be given the opportunity to take the final take-home exam will be informed by email no later than on Tuesday, December 9. If you do not receive an email you have already earned an A.

horava@berkeley.edu