Completeness relation for polarization vectors

[center o bass]

I'm reading some quantum optics and I stumbled on the following completeness relation for the polarization vectors of the electromagnetic field.

$$\sum_{a} (\epsilon_{\vec{k} a } )_i ( \epsilon^*_{ \vec{k} a} )_j = \delta_{ij} -\frac{k_i k_j}{\vec{k}^2}$$


Does anyone know how to derive this relation?

 

[dextercioby]

Check out page 36 of Cohen-Tannoudji's <Introduction to Quantum Electrodynamics>.

 

[center o bass]

Thanks! :)