Abstract
We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.
Highlights
Three-dimensional quantum electrodynamics (QED3) is an archetypal gauge field theory model of strongly interacting relativistic planar fermions
Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation
In order to compute all of these diagrams and extract from them the unrenormalized fermion self-energy of QED3 up to four loops, we first considered the corresponding results for the unrenormalized QCD quark propagator
Summary
Three-dimensional quantum electrodynamics (QED3) is an archetypal gauge field theory model of strongly interacting relativistic planar fermions. In a recent paper [7], we studied the gauge covariance of the massless fermion propagator of quenched QED3 in a linear covariant gauge in dimensional regularization We undertake this task and explicitly calculate the fermion propagator of quenched QED3 at three and four loops in an arbitrary linear covariant gauge and in dimensional regularization in d 1⁄4 3 − 2ε.
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