Name: Sam Date: 10/12/16-04:36:02 PM Z
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