  The aim of this work is to study the electron transport in graphene with
impurities by introducing a generalization of linear response theory for linear
dispersion relations and spinor wave functions. Current response and density
response functions are derived and computed in the Boltzmann limit, showing
that in the former case, a minimum conductivity appears in the no-disorder
limit. In turn, from the generalization of both functions, an exact relation
can be obtained that relates both. Combining this result with the relation
given by the continuity equation, it is possible to obtain general functional
behavior of the diffusion pole. Finally, a dynamical diffusion is computed in
the quasistatic limit using the definition of relaxation function. A lower
cutoff must be introduced to regularize infrared divergences, which allow us to
obtain a full renormalization group equation for the Fermi velocity, which is
solved up to order O(h^2).
