LKF transformations give all-order gauge-transformed fermion propagators in RQED, with ξ=1/3 eliminating one-loop leading logs and numerical checks confirming gauge-invariant condensate and pole mass.
Does the weak coupling limit of the Burden-Tjiang deconstruction of the massless quenched QED3 vertex agree with perturbation theory?
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abstract
We derive constraints on the non-perturbative 3-point fermion-boson transverse vertex in massless QED3 from its perturbative calculation to order $\alpha$. We also check the transversality condition to two loops and evaluate the fermion propagator to the same order. We compare a conjecture of the non-perturbative vertex by Burden and Tjiang against our results and comment on its draw backs. Our calculation calls for the need to construct a non-perturbative form for the fermion-boson vertex which agrees with its perturbative limit to ${\cal O}(\alpha)$.
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Landau-Khalatnikov-Fradkin Transformations in Reduced Quantum Electrodynamics: Perturbative and Nonperturbative Dynamics of the Fermion Propagator
LKF transformations give all-order gauge-transformed fermion propagators in RQED, with ξ=1/3 eliminating one-loop leading logs and numerical checks confirming gauge-invariant condensate and pole mass.