An approach that has been given promising results concerning investigations on the physics of graphene is the so-called reduced quantum electrodynamics. In this work we consider the natural generalization of this formalism to curved spaces. We employ the local momentum space representation. We discuss the validity of the Ward identity and study one-loop diagrams in detail. We show that the one-loop beta function is zero. As an application, we calculate the one-loop optical conductivity of graphene by taking into account curvature effects which can be incorporated locally. In addition, we demonstrate how such effects may contribute to the conductivity. Furthermore, and quite unexpectedly, our calculations unveil the emergence of a curvature-induced effective chemical potential contribution in the optical conductivity.
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