Levi-Civita Tensor product

  • Thread starter raopeng
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In many physics literature I have encountered, one of the properties of Levi-Civita tensor is that [itex]ε_{ijk}ε_{lmn}[/itex]is equivalent to a determinant of Kronecker symbols. However this is only taken as a given theorem and is never proved. Is there any source which has proven this property?
 

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dextercioby
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Well, the tensor product is a six index object which is always expressible as a sum of a tensor product of 3 2-index objects which must necessarily be the delta Kroneckers. The nice arrangement of this sum in a determinant cannot be proven per se, just taken for granted.
 
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I can get that intuitively the Levi-Civita tensor is deeply connected to the Kronecker symbol. But if the arrangement cannot be proved per se, how does this theorem hold true...
 

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