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Completeness relation for polarization vectors

  1. Oct 31, 2012 #1
    I'm reading some quantum optics and I stumbled on the following completeness relation for the polarization vectors of the electromagnetic field.

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

    Does anyone know how to derive this relation?
  2. jcsd
  3. Oct 31, 2012 #2


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    Check out page 36 of Cohen-Tannoudji's <Introduction to Quantum Electrodynamics>.
  4. Oct 31, 2012 #3
    Thanks! :)
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