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The conductivity of an electron gas can be alternatively calculated eitherfrom the current--current or from the density--density correlation function.Here, we compare these two frequently used formulations of the Kubo formula forthe two--dimensional Dirac electron gas by direct evaluations for severalspecial cases. Assuming the presence of weak disorder we investigateperturbatively both formulas at and away from the Dirac point. While to zerothorder in the disorder amplitude both formulations give identical results, withsome very strong assumptions though, they show significant discrepanciesalready in first order. At half filling we evaluate all second order diagrams.Virtually none of the topologically identical diagrams yield the samecorrections for both formulations. We conclude that a direct comparison ofconductivities of disordered system calculated in both formulas is notpossible.

Linear response peculiarity of a two--dimensional Dirac electron gas at weak scattering