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Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics

We derive the Landau-Khalatnikov-Frandkin transformation (LKFT) for the fermion propagator in quantum electrodynamics (QED) described within a brane-world inspired framework where photons are allowed to move in $d_γ$ space-time (bulk) dimensions, while electrons remain confined to a $d_e$-dimensional brane, with $d_e < d_γ$, referred to in the literature as reduced quantum electrodynamics, RQED$_{d_γ,d_e}$. Specializing to the case of graphene, namely, RQED$_{4,3}$ with massless fermions, we derive the nonperturbative form of the fermion propagator starting from its bare counterpart and then compare its weak coupling expansion to known one- and two-loop perturbative results. The agreement of the gauge-dependent terms of order $α$ and $α^{2}$ is reminiscent from the structure of LKFT in ordinary QED in arbitrary space-time dimensions and provides strong constraints for the multiplicative renormalizability of RQED$_{d_γ,d_e}$.