Electromagnetic responses of relativistic electrons

We compute the real and imaginary parts of the electric permittivities and magnetic permeabilities of relativistic electrons from quantum electrodynamics at finite temperatures and densities, for weak fields, neglecting electron-electron interactions. For non-zero temperatures, electromagnetic responses are reduced to one-dimensional integrals computed numerically. For zero temperature, we find analytic expressions for both their real/dispersive and imaginary/absorptive parts. As an application of our results, we obtain the dispersion relation for longitudinal electric plasmons. Present calculations support our recent claim that, at low frequencies and long wavelengths, the system will exhibit simultaneously negative electric and magnetic responses.