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 dγ space-time (bulk) dimensions, while electrons remain confined to a de-dimensional brane, with de < dγ, referred to in the literature as reduced quantum electrodynamics, RQED dγ ,de . Specializing to the case of graphene, namely, RQED4,3 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 dγ ,de .

The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with N photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths

Abstract. We evaluate the impact of an external magnetic field on the chiral symmetry and confinement-deconfinement transition temperatures by using a vectorvector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature T and magnetic field strength eB (e represents the fundamental electric charge), we determine the pseudocritical temperatures for the chiral (T Considering a lattice inspired running coupling which monotonically decreases with eB, inverse magnetic catalysis takes place in our model. We explore the role of the magnetic field in the traits of the confinement-deconfinement transition described by the model. Our findings are also in agreement with predictions derived from effective models of strong interactions.