Levi-Civita Identity Proof Help (εijk εijl = 2δkl)

[John Delaney]

Homework Statement

Prove εijk εijl = 2δkl

Relevant Equations

εijk εilm = δjl δkm - δjm δkl

I assumed that this would be a straightforward proof, as I could just make the substitution l=j and m=l, but upon doing this, I end up with:

δjj δkl - δjl δkj

= δkl - δlk

Clearly I did not take the right approach in this proof and have no clue as to how to proceed.

 

[Antarres]

Well you are right that you can do it just by making a 'substitution'. However, bear in mind that summation convention is in use here. You have to sum over the indices that are repeating. With that, you should be able to get the right result.

 

[John Delaney]

Well you are right that you can do it just by making a 'substitution'. However, bear in mind that summation convention is in use here. You have to sum over the indices that are repeating. With that, you should be able to get the right result.

Thank you for the reminder, completely forgot that δjj = 3 rather than 1.