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Summation Convention

  1. Mar 20, 2010 #1
    Hello, I think I am fundamentally confused with summation convention. For example, if I have

    [itex]
    \epsilon_{ijk}x_j\delta_{jk}
    [/itex]

    Can I sift the levi civita and get

    [itex]
    \epsilon_{ijj}x_j=0
    [/itex]

    or sift x and get

    [itex]
    \epsilon_{ijk}x_k\not=0
    [/itex]

    Each gives a different answer. What mistake am I making here?
    Thank you,

    Ian
     
  2. jcsd
  3. Mar 20, 2010 #2

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    The fundamental confusion is that you've got an index repeated three times. This is incorrect: an index can only appear once or twice, the latter meaning it is summed over.
     
  4. Mar 20, 2010 #3
    Ah I see - thanks very much

    Ian
     
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