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The polarization sum for a massless vector in vacuum may be replaced as follows: sum_{polarizations} epsilon_mu epsilon*_nu -> -g_{mu nu}

However, for a massless vector in a dense medium of charge carriers, the longitudinal and transverse polarizations are inequivalent. We have instead: sum_{polarizations, T} epsilon_mu epsilon*_nu -> delta_{ij} - k_i k_j/k_m dot k_m (where i, j, m are spatial indices only) and sum_{polarizations, L} epsilon_mu epsilon*_nu -> -g_{mu nu} + k_mu k_nu/k_rho dot k_rho - delta_{ij} + k_i k_j/k_m dot k_m

So when I contract a Dirac trace against the photon polarizations, I have something other than a metric tensor or a vector to deal with (since I have to separate the spatial and temporal components to calculate the transverse mode).

Please let me know if this is enough information, otherwise I can explicitly construct the trace I am interested in.

Thank you for your help,

Sam

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