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Using suffix notation to find alternative expressions

  1. Oct 4, 2013 #1

    ppy

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    1. The problem statement, all variables and given/known data
    use the relationship ε[itex]_{ijk}[/itex] ε[itex]_{klm}[/itex]=δ[itex]_{il}[/itex]δ[itex]_{jm}[/itex]-δ[itex]_{im}[/itex]δ[itex]_{jl}[/itex] to find an alternative expression for ε[itex]_{ijk}[/itex]ε[itex]_{ilm}[/itex]. Hence simplify ε[itex]_{ijk}[/itex]ε[itex]_{ijm}[/itex]

    2. Relevant equations


    I know that the kronecker delta is 1 for i=j and 0 for i not equal to j. and that the alternating tensor is 0 for any I,j,k equal. +1 if (I,j,k)= (1,2,3) or (2,3,1) or (3,1,2) and -1 for (3,2,1) or (1,3,2) 0r (2,1,3). I also know that the alternating tensor is unchanged under cyclic permutations of its suffices. I know I am supposed to use all these facts but I am unsure how.


    Help would be appreciated.

    Thanks.
     
  2. jcsd
  3. Oct 4, 2013 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    hi ppy! :smile:


    in εijkεklm, the common index is 3rd and 1st

    in εijkεilm, the common index is 1st and 1st

    so use a cycllc permutation to make it 3rd and 1st :wink:
     
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