Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics

TL;DR

This paper derives the Landau-Khalatnikov-Fradkin transformation for fermion propagators in reduced quantum electrodynamics, specifically applied to graphene, and compares nonperturbative results with perturbative calculations to explore renormalizability.

Contribution

It provides the first derivation of LKFT in RQED with arbitrary dimensions and applies it to graphene, linking nonperturbative and perturbative results.

Findings

Agreement of gauge-dependent terms at order α and α² with perturbative results.

Constraints on the multiplicative renormalizability of RQED.

Nonperturbative fermion propagator form derived for RQED$_{4,3}$.

Abstract

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, RQED$_{d_\gamma,d_e}$. 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 $\alpha$ and $\alpha^{2}$ 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$_{d_\gamma,d_e}$.