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We analyze the concept of causality for the conductivity of graphenedescribed by the Dirac model. It is recalled that the condition of causalityleads to the analyticity of conductivity in the upper half-plane of complexfrequencies and to the standard symmetry properties for its real and imaginaryparts. This results in the Kramers-Kronig relations, which explicit formdepends on whether the conductivity has no pole at zero frequency (as in thecase of zero temperature when the band gap of graphene is larger than twice thechemical potential) or it has a pole (as in all other cases, specifically, atnonzero temperature). Through the direct analytic calculation it is shown thatthe real and imaginary parts of graphene conductivity, found recently on thebasis of first principles of thermal quantum field theory using thepolarization tensor in (2+1)-dimensional space-time, satisfy the Kramers-Kronigrelations precisely. In so doing, the values of two integrals in the commonlyused tables, which are also important for a wider area of dispersion relationsin quantum field theory and elementary particle physics, are corrected. Theobtained results are not of only fundamental theoretical character, but can beused as a guideline in testing the validity of different phenomenologicalapproaches and for the interpretation of experimental data.

Kramers-Kronig relations and causality conditions for graphene in the framework of the Dirac model