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 $d_{\gamma }$ space-time (bulk) dimensions, while electrons remain confined to a $d_e$-dimensional brane, with $d_e<d_{\gamma }$, referred to in the literature as reduced quantum electrodynamics, ${\mathrm{RQED}}_{d_{\gamma },d_e}$. Specializing to the case of graphene, namely, ${\mathrm{RQED}}_{4,3}$ 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 at order $\alpha$ and ${\alpha }^2$ is reminiscent of the structure of LKFT in ordinary QED in arbitrary space-time dimensions and provides strong constraints for the multiplicative renormalizability of ${\mathrm{RQED}}_{d_{\gamma },d_e}$.

• Received 13 April 2016

DOI:https://doi.org/10.1103/PhysRevD.93.094035