1. Limited time only! Sign up for a free 30min personal 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!

Pauli matrices and the Levi-Civita tensor : commutation relations

  1. Oct 21, 2013 #1
    1. The problem statement, all variables and given/known data
    Whats up guys!

    I've got this question typed up in Word cos I reckon its faster:
    http://imageshack.com/a/img5/2286/br30.jpg [Broken]

    2. Relevant equations

    I don't know of any

    3. The attempt at a solution
    I dont know where to start!!! can u guys help me out please?

    Thanks!
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Oct 21, 2013 #2
    You can start by multiplying each possible combination of pauli matrices. Do that and factor out a 1 or -1, which can be replaced with a Levi-Cevita symbol. Use i = 1, j = 2, k = 3.
     
  4. Oct 21, 2013 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure, just check it by putting the matrices into the commutation relation. For example, show ##[\sigma_1,\sigma_2]=\sigma_1 \sigma_2-\sigma_2 \sigma_1=i\sigma_3##. But it's not going work very well until you fix ##\sigma_3##. That's not a Pauli matrix.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Pauli matrices and the Levi-Civita tensor : commutation relations
Loading...