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cashmerelc
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Homework Statement
Prove [tex]\sum_{j,k}[/tex] [tex]\epsilon_{ijk}[/tex] [tex]\epsilon_{ljk}[/tex] = 2[tex]\delta_{il}[/tex]
Homework Equations
[tex]\epsilon_{ijk}[/tex] [tex]\epsilon_{ljk} = [tex]\delta_{il}[/tex]([tex]\delta_{jj}[/tex][tex]\delta_{kk}[/tex] - [tex]\delta_{jk}[/tex][tex]\delta_{kj}[/tex]) + [tex]\delta_{ij}[/tex]([tex]\delta_{jk}[/tex][tex]\delta_{kl}[/tex] - [tex]\delta_{jl}[/tex][tex]\delta_{kk}[/tex]) + [tex]\delta_{ik}[/tex]([tex]\delta_{jl}[/tex][tex]\delta_{kk}[/tex] - [tex]\delta_{jj}[/tex][tex]\delta_{kl}[/tex])
The Attempt at a Solution
Okay, in cases where subscripts of the Kronecker delta are equal, then [tex]\delta_{jj}[/tex] = 1.
If the subscripts are not equal, then [tex]\delta_{il}[/tex] = 0.
So plugging those into the parenthesis of the above equation gives me:
[tex]\delta_{il}[/tex]([tex]\delta_{jj}[/tex][tex]\delta_{kk}[/tex]) ?
If that is the case, then how could the two inside the parenthesis equal 2? I know I must be missing something.
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