Physics 221A, Fall 2007

The final is here.  Solutions; figures for solutions

Corrections and notes:

In problem 2 you want the beta function in d=4.

Problem 3b should read "Find the unbroken symmetry..."

Open notes, homework, solutions, Srednicki (the text, not the person).  Please do not discuss the test with anyone but me before the due time.  I will check my email regularly, and post any corrections/clarifications on the course web page.}

Begin: Tuesday, Dec. 11, noon.

Due: Wednesday, Dec. 12, noon in my office, KITP 2319 (except for those who have made other arrangements).

T-Th 9:30-10:45, Bldg. 387, Rm. 104 (this is a `temporary' building south of Davidson library - see map - I've never taught there before).

Instructor:  Joe Polchinski,  joep@kitp.ucsb.edu
Office hours: Th 3:30-4:30,  KITP 2319 (or email or talk to me after class, to set up another time).  I am also happy to answer questions by email.

TA: Jorge Rocha, Office hours W 2:00-3:30, F 10:30-12:00, PLC

I will roughly cover Part I of Srednicki, Quantum Field Theory (quantization of spin zero fields). 

Quantum field theory is a hard subject (though Srednicki and I will do our best to make it seem easy), so it is often helpful to have other texts to give a different perspective.  Some that you may find useful: Peskin & Schroeder, An Introduction to Quantum Field Theory;  Weinberg, The Quantum Theory of Fields, I, II, III;  Zee, Quantum Field Theory in a Nutshell;  Ryder, Quantum Field Theory;  Ramond, Field Theory: A Modern Primer.  I often find Peskin and Schroeder helpful, especially if I want to go into a bit more depth on some topic.  Weinberg is encyclopedic, and a good reference.  Zee is fun - it is not systematic enough to teach from, but good for the highlights.  Ryder and Ramond are clear but a bit terse, there is less discussion.

I will also scan and post my notes, but I warn you that these are not at all polished, they may just be outlines.

Grading will be based 50% on weekly homeworks and 50% on the final exam.  Homeworks will generally be due Fridays at 5 pm in the TA's mailbox, 5th floor Broida.  Homework turned in by 5pm the following Monday will be penalized 10%; homework turned in up to one week late will be penalized 20%; no later homework can be accepted.  Contact me if there is good reason for an exception.

ANNOUNCEMENTS (updated Tuesday 3:15 pm):

1.  I will cover non-linear sigma models and large-N in the final regular class Thursday, and conformal symmetry and the operator product expansion in a Friday makeup lecture (attendance optional, 1:30-3:00, KITP small seminar room).  See syllabus below for Thursday and Friday references.

2. Final exam: out: noon Tues. 12/11, in: noon Weds. 12/12.  Other times can be arranged for those with conflicts.

Homework #1 (due 10/5) Solutions
Homework #2 (due 10/12) Solutions
Homework #3 (due 10/19) Solutions
Homework #4 (due 10/26) Solutions
Homework #5 (due 11/2) Solutions
Homework #6 (due 11/9) Solutions
Homework #7 (due 11/16) Solutions
Homework #8 (due 11/30) Solutions
Homework #9 (due 12/7) Solutions

FAQ  (Questions I've been asked, which may be of more general interest)

Th 9/27: What is Quantum Field Theory and why is it so important?  Examples: canonical quantization of the Klein-Gordon field; `second quantization' of the Schrodinger equation (Sred. ch. 1, 3; P&S 2).   Lecture 1 notes
T 10/2: Continue with canonical quantizaton of the scalar field.  Vacuum energy, renormalization preview.  Lecture 2 notes
Th 10/4: Lorentz invariance, spin-statistics (Sred. ch. 2, 4).  Lecture 3 notes
T 10/9: Begin path integral quantization, QM: ch. 6,7 (we will come back to LSZ later).  Lecture 4 notes (these follow the text pretty closely)
Th 10/11: Finish path integral for QM (ch. 7).  Path integral for free field theory (ch. 8).  Lecture 5 notes
T 10/16: Path integral for interacting field theory (ch. 9).  Lecture 6 notes
Th 10/19: Disconnected, vacuum, tadpole graphs; counterterms; correlation functions; Feynman rules in position and momentum space (ch. 10).  Lecture 7 notes
T 10/23: The S-matrix and the LSZ formula (ch. 5, 10).  Lecture 8 notes.  My derivation of LSZ was based on P&S 7.2.  Mark also recommends these LSZ lecture notes from John Collins (Penn State).
Th 10/25: Cross sections and decay rates (ch. 11).  Also read ch. 12, dimensional analysis.  Lecture 9 notes
T 10/30: The one-loop correction to the propagator: evaluating loop graphs - Feynman trick, dimensional reg. (ch. 14).  Lecture 10 notes
Th 11/1: Finish loop graph, do geometric propagator sum (ch. 14).  Relation to spectrum (ch. 13, 15).  Lecture 11 notes
T 11/6: Vertex and other 1PI corrections (ch. 16, 17) Renormalization power counting (ch. 18).  Lecture 12 notes
Th 11/8: IR divs. (ch. 26) Renormalization group (ch. 27, 28).  Lecture 13 notes
T 11/13: Continue renormalization group (ch. 27, 28).  Lecture 14 notes
Th 11/15: Effective field theory (ch. 29).  Lecture 15 notes
T 11/20: No Class
T 11/27: Continuous symmetries: Noether, Ward, energy-momentum tensor (ch. 22) Coleman-Mandula argument.  Lecture 16 notes
Th 11/29: Discrete symmetries (ch. 23).  Non-Abelian symmetries (ch. 24).  Lecture 17 notes
T 12/4: Spontaneous breaking of discrete (ch. 30) and continuous (ch. 32) symmetries.  Goldstone and Mermin-Wagner-Coleman theorems.  Lecture 18 notes
Th 12/6: Non-linear sigma models and the large-N (vector) limit.  Reference: 1/N, Sidney Coleman  (Sec. 2.1 and 2.3.  The model we will study is simpler than in 2.3: it has no A_\mu field.)  Lecture 19 notes
F 12/7, 1:30, KITP Small Seminar Room:  Optional makeup lecture: conformal invariance and the operator product expansion.  Some notes on conformal symmetry: 1, 2.  These are taken from Itzykson and Zuber, sec. 13.2.1.  Lecture 20 notes