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 sub([gamma]) space-time (bulk) dimensions, while electrons remain confined to a d sub(e)dimensional brane, with d sub(e) d sub([gamma]), referred to in the literature as reduced quantum electrodynamics, RQED sub()dgamma],de Specializing to the case of graphene, namely, RQED sub(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] super(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 RQED sub()dgamma],de