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We compute the real and imaginary parts of the electric permittivities andmagnetic permeabilities for relativistic electrons from quantum electrodynamicsat finite temperature and density. A semiclassical approximation establishesthe conditions for neglecting nonlinear terms in the external electromagneticfields as well as electron-electron interactions. We obtain both the electricand magnetic responses in a unified manner and relate them to longitudinal andtransverse collective plasma oscillations. We demonstrate that such collectivemodes are thresholds for a metamaterial regime of the electron plasma whichexhibits simultaneously negative longitudinal permittities and permeabilities.For nonzero temperatures, we obtain electromagnetic responses given byone-dimensional integrals to be numerically calculated, whereas for zerotemperature we find analytic expressions for both their real/dispersive andimaginary/absorptive parts.

Finite-temperature electromagnetic responses of relativistic electrons