d Xie Chen - Physics 129b

Physics 129b

Group Theory, Winter 2020


  • Prof. Xie Chen
  • Office: 163 W. Bridge
  • Mail Code: 149-33
  • Phone: x3793
  • Email: xiechen[at]caltech[dot]edu
  • Office hour: Wednesday, 4-5pm


  • Linear algebra, matrix
  • Differential equation
  • Basics of classical and quantum physics.


  • Tuesdays 9:00 am - 10:30 am, 107 Downs
  • Thursdays 9:00 am - 10:30 am, 107 Downs
  • First lecture, Jan. 7, 2020

Recommended Text Book

    (not required, can be used for reference reading, homework and exam)
  • A. Zee, Groups, Group Theory in a Nutshell for Physicists, Princeton University Press, 2016.
  • P. Ramond, Group Theory: A Physicist’s Survey, Cambridge Univ. Press, 2010.
  • H. F. Jones, Groups, Representations, and Physics, Institute of Physics Publishing, 2nd ed.,
  • J. F. Cornwell, Group Theory in Physics: An Introduction, Academic Press, 1997.
  • 1998.
  • Wu-Ki Tung, Group Theory in Physics, World Scientific, 1985.
  • H. Georgi, Lie Algebras in Particle Physics, Benjamin, 1982.
  • E. P. Wigner, Group Theory, Academic Press, 1959.
  • J. Talman, Special Functions, a Group-Theoretic Approach, Benjamin, 1968.
  • M. Tinkham, Group Theory and Quantum Mechanics, 1964.

Problem Sets

Posted here every Thursday, due on the following Thursday by 5pm. Please put finished homework in a mail slot marked 'Ph129b Inbox' in Bridge Annex. Solutions will be posted on this website.

Graded problem sets can be picked up in a mail slot marked 'Ph129b Outbox' in Bridge Annex one week after the due date.


Final exam in the week of Mar. 16, 2019. The exam will be take-home and "limited" open-book (only textbooks and class notes allowed).


60% problem sets, 40% final exam.

Homework and exam are governed by the honor system.

Teaching Assistants

  • Chi-Fang (Anthony) Chen, chifang[at]caltech.edu
  • Nabha Shah, nnshah[at]caltech.edu
  • Recitation and office hour: Tuesday 6pm - 8pm, 269 Lauritsen.


  • General properties of groups (subgroup, coset, quotient group, homomorphism, direct product)
  • Group representations (Irreducible representation, properties, CG coefficient)
  • Finite groups (permutation groups, cyclic groups, classification)
  • Lie groups (SO(3), SU(2), Lie algebra, general properties of simple Lie groups)
  • Application: atomic spectra
  • Application: condensed matter
  • Application: special relativity
  • Application: standard model

Lecture Notes

Problem Sets and solutions


OFFICIAL policy:

  • Work (the entire problem set) will be accepted up to one week late at 1/2 credit, no credit thereafter. Please put a note at the top of your problem set if it is late.
  • Students may request extensions from the corresponding grader (see emails above) a day or more in advance. Extension requests are governed by the honor system.
  • One extension (for up to one week) is allowed without question (your silver bullet). Please put a note at the top of your problem set that you are using your silver bullet.
  • Extension requests should be accompanied by a good excuse (eg, physical or mental illness), and in principle should be accompanied by a letter from a doctor or the dean.
  • Please put late or extension problem sets in the corresponding grader's mail box, and email them.
  • Late papers make far more work for the graders, who have their own set of pressures and deadlines as graduate students. There is no entitlement to extensions, so please do not be demanding.

Honor Code and Collaboration Policy

  • Work is governed by the honor system.
  • You may not use sources that contain the answer to a problem or to a very similar problem.
  • In particular, do not use solution sets from previous years, or problem/solution books, at any time. Exams and their solutions from past years are not to be used in any fashion.
  • Discussion with others is encouraged, but then you should go off alone and write it up; the work you hand in must be your own.
  • Mathematica may be used in problem sets, or in exams for getting past some mathematical chore (not for gaining knowledge of the physics). Make sure you simplify the result as much as possible, so that it is easy to see what the math is telling you.