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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?

    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


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    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.
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