I Is the Kroneker Delta Identity Used Correctly in this Paper?

Safinaz
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A question about a Kroneker Delta identity
Is there a Kroneker Delta identity:

$$ \delta^3 (k) \delta^3 (k) = \frac{2\pi^2}{k^3} ~ \delta (k_1- k_2) $$?

Where k is a wave number. In this Paper: Equations 26 and 27, I think this identity is used to make ##k_1=k_2## and there is an extra negative sign.
 
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Could you tell us what is the relation among k, k_1 and k_2 ?
Assuming they have same dimension k, dimension of LHS is k^-6 that of RHS is k^-4. They do not coincide.
 
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First of all you must clearly distinguish between a Kronecker (sic!) ##\delta## and Dirac ##\delta## distributions, which refers to discrete variables, i.e.,
$$\delta_{k_1 k_2}=\begin{cases} 1 &\text{for} \quad k_1=k_2, \\
0 &\text{for} k_1 \neq k_2. \end{cases}
$$
Then you have ##\delta_{k_1k_2}^2=\delta_{k_1 k_2}##.

For Dirac-##\delta## distributions the square doesn't make any sense. Whenever it occurs somewhere, the authors make a mistake. In the paper you linked, nowhere is such a non-sensical formula though!
 
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