Abstract
We study the gauge-covariance of the massless fermion propagator in reduced Quantum Electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin transformation. We find that the weak coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one.
Highlights
The Landau-Khalatnikov-Fradkin (LKF) transformation [1] is an elegant and powerful transformation allowing one to study the gauge-covariance of Green’s functions in gauge theories
We study the gauge-covariance of the massless fermion propagator in reduced quantum electrodynamics (QED)
We prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one
Summary
The Landau-Khalatnikov-Fradkin (LKF) transformation [1] (see [2,3]) is an elegant and powerful transformation allowing one to study the gauge-covariance of Green’s functions in gauge theories. In its original form, the LKF transformation was applied to the fermion propagator (and to the fermion-photon vertex that will not be discussed here) of four-dimensional quantum electrodynamics (QED4), which is the primary example of an Abelian gauge field theory. Since it has been extensively used in studies of QED in various dimensions, see, e.g., [4,5,6,7,8,9,10,11] and, more recently, in their generalization to brane worlds [12] that we shall come back to in the following and to non-Abelian SUðNÞ gauge field theories [13,14]. Various other choices of scales are presented in Appendix A and in Appendix B the LKF transformation for reduced scalar QED is derived
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