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Homework Help: Kronecker delta in index notation

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data

    what does the expression [tex]\delta_{ii}[/tex] mean?

    2. Relevant equations

    [tex]\delta_{ij}=1[/tex] if i = j and 0 otherwise

    3. The attempt at a solution
    What i'm not sure about is if both indices are in the subscript does this mean i can only use it on a term with a subscript or can it also act on a term with a superscript? what is the difference between this and [tex]\delta^{j}_{i}[/tex]? and why can't it be used for index replacement?
     
  2. jcsd
  3. Feb 10, 2010 #2

    HallsofIvy

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    Science Advisor

    The standard convention (often called the "Einstein summation convention" because Albert Einstein introduced it to simplify equations in his "General Theory of Relativity") is that when an index is repeated, it implies a sum over all possible values of that index.

    Representing the Kroneker delta as a matrix, you get, in n dimensions, the n by n identity matrix. In that case [itex]\delta_{ii}[/itex] is the sum of the main diagonal (often called the "trace") and is equal to n.
     
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