Physics 221C, Spring 2007

MWF 10:00-10:50, North Hall 1109

Instructor:  Joe Polchinski,  joep@kitp.ucsb.edu
Office hours: Thurs., 3:30 - 4:30,  KITP 2319

TA: Richard Eager, Office hours Monday: 2-3, Wednesday: 3-4, Friday: 11-12

Final Exam: Available Noon Weds. here (and at KITP 2319), Due Noon Thurs. at KITP 2319.  Open Srednicki, Peskin & Schroeder, Weinberg, notes, homeworks, solutions.  Apologies: the exam was not posted until 12:10, so feel free to take 10 extra minutes!

Final Exam solutions (final version) Graphs for Solution to #4

Mathematica - change of policy: I don't think you need it, but I would rather you use it than waste time on mindless algebra.  However, I will give extra credit for a nice analytic solution, which is possible in, e.g., problem 2.

Corrections:

In problem 1, g' has different units from g_2 so they can't be equal!  Leave the answer in terms of g'.

On problem 2, the momentum should not be perpendicular to the 3-direction - that is, k_3 is not zero.
The problem asked that it not be parallel.  In fact, when you look for the eigenvalues of M, I suggest that you boost to a frame in which k_1 = k_2 = 0 --- but explain why you can do this without messing up A_3 = 0.

Problem 4 is in 4 dimensions, in case that is not clear.  I will be impressed if anyone gets close to the whole thing.  Start by doing a smaller part as carefully as possible - such as the term with two g-vertices and no g'-vertices.

Also problem 4 - I left the m^2 out of the propagator that I gave you.

I will follow selected chapters from Srednicki, Quantum Field Theory for most of the quarter.  The textbooks by Weinberg and by Peskin & Schroeder provide useful additional perspectives on many subjects.  Last 4 lectures: Sidney Coleman's Erice lecture on 1/N.

Homework #1  Note: in problem 5, you want Landau gauge, not Feynman (in Feynman gauge there is a gauge piece).  Thanks to Matt Block.
Homework #2  PS 6.3  Note: in probs. 2 and 3, assume four dimensions.  In prob. 3, `problem 3 of the last set' should be `problem 2 of this set.'
Homework #3
Homework #4
Homework #5  Prob. 2 diagrams
Homework #6  PS 19.1
Homework #7
Homework #8
Homework #9  A short assignment.




M 4/2: QED loops, vacuum polarization graph (Sred. 62)
W 4/4: Physics of vacuum polarization; renormalization scheme; analyticity properties.
F 4/6: QED beta function; Landau pole (Sred. 62, 66)

M 4/9: More on RG.  Intro to electron/muon magnetic moment (Sred. 63, 64)
W 4/11: Electron/muon magnetic moment calculation.
F 4/13: Magnetic moment discussion, bounds on new physics (see F. Jegerlehner, hep-ph/0703125 for latest comparison of theory and experiment).
Effective field theory (Sred. 29, Weinberg 12.3)

M 4/16: NO CLASS.  Makeup will be scheduled.
W 4/18: Finish magnetic dipole moment, discuss electric dipole moment.
F 4/20: Infrared and collinear divergences (Peskin 6.4, 6.5, beginning of 17.5; or Weinberg 13.1 to 13.4).

M 4/23: Begin Non-Abelian gauge theories (Sred. 24, 69, 70).
W 4/25: Continue Non-Abelian gauge theories.  Some Lie algebra.
F 4/27: Representations of Lie algebras (Sred. 70).

M 4/30: Quantization of Non-Abelian gauge theories (ghosts)
W 5/2, F 5/4: QCD beta function, RG flows in various gauge theories (Sred. 71-73).

M 5/7 - F 5/11: Global symmetries of QCD, chiral symmetries, anomalies in 2d and 4d.  (Sred. 83, 75, 76, 77)

M 5/14: Chiral symmetry breaking, effective Lagrangians (Sred. 83)
W 5/16: Higgs mechanism (Sred. 84-86)
W 5/16, 5:00 to 7:00: Makeup Lecture, KITP auditorium, Lattice gauge theory and confinement (Sred. 82).
F 5/18: Higgs mechanism (Sred. 84-86) Phases of gauge theories (a somewhat technical reference is Gerard 't Hooft, Nucl.Phys.B138:1,1978).

M 5/21: Fermion masses from spontaneous breaking; anomalies in gauge symmetries (Sred. 75); gauge and Higgs sector of Standard Model (Sred. 87).
W 5/23: NO CLASS.
F 5/25: Lepton and quark sectors of Standard Model (Sred. 88, 89)

M 5/28: Memorial Day Holiday
W 5/30: Finish Standard Model: CKM matrix, anomaly cancellation, neutrino masses
F 6/1, M 6/4, W 6/6, F 6/8: The 1/N Expansion.  Primary reference: Sidney Coleman's Erice lecture (also reprinted in his book Aspects of Symmetry).



The main focus of the course will be the quantum field theory behind the Standard Model.