1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Representations of SO(3)

  1. Jan 28, 2008 #1
    Hi all, I asked this on the Quantum Physics board but didn't get a response.

    I'm reading Cahn's book on semi-simple lie algebras and their representations.

    http://www-physics.lbl.gov/~rncahn/book.html

    In chapter 1, he attempts to build a (2j+1)-dimensional representation [itex]T[/itex] of the Lie algebra of SO(3) starting with the abstract commutation relations

    [itex][T_z,T_+] = T_+, \quad [T_z,T_-] = - T_-,\quad [T_+,T_-] = 2T_z[/itex] Eq (I.14).

    He begins by defining the action of [itex]T_z,T_+[/itex] on the vector [itex]v_j[/itex] by

    [itex]T_z v_j = j v_j, \quad T_+ v_j = 0[/itex]

    but he does not explain what the [itex]v_j[/itex]'s are. How does one even know that such vectors exist?

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Jan 28, 2008 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [EDIT]I've decided to answer on the quantum physics forum[/EDIT]
     
    Last edited: Jan 28, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Representations of SO(3)
Loading...