We derive the polarization tensor of graphene at nonzero temperature in (2+1)-dimensional space-time. The obtained tensor coincides with the previously known one at all Matsubara frequencies, but, in contrast to it, admits analytic continuation to the real frequency axis satisfying all physical requirements. Using the obtained representation for the polarization tensor, we develope quantum field theoretical description for the reflectivity of graphene. The analytic asymptotic expressions for the reflection coefficients and reflectivities at low and high frequencies are derived for both independent polarizations of the electromagnetic field. The dependencies of reflectivities on the frequency and angle of incidence are investigated. Numerical computations using the exact expressions for the polarization tensor are performed and application regions for the analytic asymptotic results are determined.

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The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and outof-plane conductivities of graphene are expressed via the components of the polarization tensor in (2+1)-dimensional space-time analytically continued to the real frequency axis. Simple analytic expressions for both the real and imaginary parts of the conductivity of graphene are obtained at zero and nonzero temperature. They demonstrate an interesting interplay depending on the values of mass gap and chemical potential. In the local limit, several results obtained earlier using various approximate and phenomenological approaches are reproduced, refined and generalized.The numerical computations of both the real and imaginary parts of the conductivity of graphene are performed to illustrate the obtained results. The analytic expressions for the conductivity of graphene obtained in this paper can serve as a guide in the comparison between different theoretical approaches and between experiment and theory.

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