  The conductivity of an electron gas can be alternatively calculated either
from the current--current or from the density--density correlation function.
Here, we compare these two frequently used formulations of the Kubo formula for
the two--dimensional Dirac electron gas by direct evaluations for several
special cases. Assuming the presence of weak disorder we investigate
perturbatively both formulas at and away from the Dirac point. While to zeroth
order in the disorder amplitude both formulations give identical results, with
some very strong assumptions though, they show significant discrepancies
already in first order. At half filling we evaluate all second order diagrams.
Virtually none of the topologically identical diagrams yield the same
corrections for both formulations. We conclude that a direct comparison of
conductivities of disordered system calculated in both formulas is not
possible.
