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I Photon Polarization

  1. Feb 17, 2017 #1
    Hello! I am a bit confused about the completeness relation for photon polarization. So it says ## \sum_{s=1,2}\epsilon_i^s\epsilon_j^{s*}=\delta_{ij}-p_ip_j##, with ##p_i, p_j## - unit vectors. So I am not sure what are the indices i and j. I though that they represent the component of the vector, but in that case the RHS would be always 0. So what are i and j? Thank you!
     
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  3. Feb 17, 2017 #2

    Orodruin

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    Why do you think the RHS would be zero?
     
  4. Feb 17, 2017 #3
    if i=j, ##\delta_{ij}=0## and ##p_ip_j=0## as ##p_i=(1,0,0)## and ##p_j=(0,1,0)##, for example. If i=j, ##\delta_{ii}=1## and ##p_ip_i=1## so in both cases the difference is 0, right?
     
  5. Feb 17, 2017 #4

    Orodruin

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    Not right. ##p## is a fixed vector, ##p_i## is its ith component.
     
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