Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions

摘要

We explore the dependence of fermion propagators on the covariant gaugefixing parameter in quantum electrodynamics (QED) with the number of spacetimedimensions kept explicit. Gauge covariance is controlled by the theLandau-Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature,the LKFT for a fermion propagator in Minkowski space is solved exactly. Thespecial scenario of 3D is used to test claims made for general cases. Whenrenormalized correctly, a simplification of the LKFT in 4D has been achievedwith the help of fractional calculus.