In the Comment by Bordag et al. [Phys. Rev. B 113, 207401 (2026)], concerns are raised about the validity of the results presented by Rodriguez-Lopez et al. [Phys. Rev. B 111, 115428 (2025)], where the theoretical descriptions of the electric conductivity of graphene obtained from the Kubo formula and from quantum field theory via the polarization tensor are compared. In this Reply, we show that these concerns arise from misinterpretations of our work, in which the results are either inaccurately represented or applied outside the domain of validity of the model. We address the comments concerning the derivation of the Luttinger formula for the electric conductivity from the Kubo formula and clarify why the results of our work cannot be arbitrarily extended to make claims on the gauge invariance. We further demonstrate that our findings are fully consistent with the established and widely accepted literature cited in the Comment. We confirm that the model for electric conductivity discussed in our work correctly predicts a vanishing electric current in the absence of an external electric field, as physically required, and in contrast to the model advocated by the Authors of the Comment. We also show that the electric permittivity does not exhibit a double pole in $\omega$, contrary to the claim made in the Comment. Finally, we emphasize that the inclusion of losses is a standard and well-established approach in the study of transport properties of materials, including graphene, and we take the opportunity to correct a few minor typographical errors in our work. We show and maintain that all results derived in our work are fully valid and correct.

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• Electrical conductivity
• Quantum field theory
• Graphene
• Linear response theory