Abstract
Dispersion relations and sum rules are obtained for a gaseous insulating medium, under the influence of a weak constant external magnetic field. The application of the causality principle to the constitutive equation of the medium together with the behavior of free electrons in the high-frequency limit give the analytic behavior of the optical constants in the upper half complex plane, new dispersion relations, and new sum rules. The fact that the average refractive index, as well as the difference of the complex refractive indices of right and left circularly polarized waves, satisfies dispersion relations is justified by the application of relativistic causality.
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