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Homework Help: Kronecker Delta

  1. Mar 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Simplify/Evaluate these expressions involving the Kronecker delta, using Einstein's summation convention:
    a)[tex]\delta_{qr}[/tex][tex]\delta_{rp}[/tex][tex]\delta_{pq}[/tex]
    b)[tex]\delta_{pp}[/tex][tex]\delta_{qr}[/tex][tex]\delta_{rq}[/tex]

    2. Relevant equations
    [tex]\delta_{ij}[/tex]=0 when i =/= j
    [tex]\delta_{ij}[/tex]=1 when i = j


    3. The attempt at a solution
    a)[tex]\delta_{qr}[/tex][tex]\delta_{rp}[/tex][tex]\delta_{pq}[/tex]
    =[tex]\delta_{qp}[/tex][tex]\delta_{pq}[/tex]
    =[tex]\delta_{qq}[/tex] = 3 (summation over repeated q)

    b)[tex]\delta_{pp}[/tex][tex]\delta_{qr}[/tex][tex]\delta_{rq}[/tex]
    =[tex]\delta_{pp}[/tex][tex]\delta_{qq}[/tex]
    =(3)(3)
    =9
    [Am I actually able to evaluate the [tex]\delta_{qr}[/tex][tex]\delta_{rq}[/tex] part before the [tex]\delta_{pp}[/tex] part, I mean you can't do that with matrices... :S]


    Thank you
     
  2. jcsd
  3. Mar 14, 2010 #2

    phyzguy

    User Avatar
    Science Advisor

    I think what you did is correct. If you think of them as matrices, remember they are identity matrices, so they commute with everything, so the order does not matter.
     
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