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We investigate the dispersion of a classical electromagnetic field in arelativistic ideal gas of charged bosons using scalar quantum electrodynamicsat finite temperature and charge density. We derive the effectiveelectromagnetic responses and the electromagnetic propagation modes thatcharacterize the gas as a left-handed material with negative effective index ofrefraction $n_{\rm eff}=-1$ below the transverse plasmon frequency. In thecondensed phase, we show that the longitudinal plasmon dispersion relationexhibits a roton-type local minimum that disappears at the transitiontemperature.

Negative refraction and rotons in the relativistic Bose gas