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Polarization Vector for Quantum EM Field

  1. Sep 10, 2006 #1
    I'm doing some calculations and I've run into something rather strange.

    I need to evaluate the following dot products

    [tex]\vec{\epsilon}_{k,\,s}\cdot\vec{\epsilon}_{-k,\,s'} = ?[/tex]
    [tex]\vec{\epsilon}_{k,\,s}^*\cdot\vec{\epsilon}_{-k,\,s'}^* = ?[/tex]​

    where [itex]\vec\epsilon_{k,\,s}[/itex] is the normalized polarization vector for a single photon with momentum [itex]k[/itex], and spin [itex]s[/itex]. Does anyone know where I can look for these identities?
  2. jcsd
  3. Sep 10, 2006 #2

    Dr Transport

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    Assume that the polarizations are along cartesian directions......
  4. Sep 11, 2006 #3

    Meir Achuz

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    If by "spin", you mean helicity, the e.e'=plus or minus 1, depending on the relative helicities. This works because the momenta are = and opposite.
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