Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency omega, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter gamma similar or equal to 3 eV, but much larger than the collision rate tau(-1). The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv(0) << T << omega is equal to sigma(omega,k)=e(2)/4 (h) over bar and independent of the and structure parameters gamma and nu(0). Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.