Conductivity of interacting massless Dirac particles in graphene: Collisionless regime

We provide detailed calculation of the ac conductivity in the case of 1/r Coulomb interacting massless Dirac particles in graphene in the collisionless limit when omega >> T. The analysis of the electron self-energy, current vertex function, and polarization function, which enter into the calculation of physical quantities including the ac conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and 't Hooft by taking the spatial dimension D=2-epsilon for epsilon>0. The procedure adopted here yields a result for the conductivity correction which, while explicitly preserving charge conservation laws, is nevertheless different from the results reported previously in literature.