Hi,
sorry for the late reply. I'm afraid that this is not something one can
easily achieve with FeynCalc. By default FeynCalc doesn't distinguish
between upper and lower indices, which is crucial for working with
Cartesian vectors. One can of course start writing some own code on top
of FeynCalc, but very soon it quite messy and error-prone.
Unless you find a good way to rewrite things in a covariant way, working
with Cartesian vectors is not supported out of the box.
Cheers,
Vladyslav
Am 12.10.2016 um 16:36 schrieb Sam:
> 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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