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Tensors index notation

  1. Sep 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove the following relationship:

    [tex]\epsilon[/tex]pqi[tex]\epsilon[/tex]pqj = 2[tex]\delta[/tex]ij

    2. Relevant equations



    3. The attempt at a solution

    All I have so far is the decomposition using the epsilon-delta

    [tex]\epsilon[/tex]pqi[tex]\epsilon[/tex]pqj = [tex]\epsilon[/tex]qip[tex]\epsilon[/tex]pqj
    [tex]\epsilon[/tex]qip[tex]\epsilon[/tex]pqj = [tex]\delta[/tex]qp[tex]\delta[/tex]iq - [tex]\delta[/tex]qj[tex]\delta[/tex]iq

    have no idea where to turn next
     
  2. jcsd
  3. Sep 10, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    Hi vortmax, do you have a definition for the eijk (levi cevita) and understand the summation?

    You could do it reasonably simply just by evaluating ij cases for both the levi cevitas & kronecka deltas (probably all you really need to do is i=j & i<>j cases)
     
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