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

TL;DR

This paper derives an exact solution for the Landau-Khalatnikov-Fradkin transformation of the fermion propagator in QED across arbitrary dimensions, revealing gauge dependence and simplifying the transformation in 4D using fractional calculus.

Contribution

It provides the first exact solution of the LKFT for fermion propagators in Minkowski space and introduces a fractional calculus approach to simplify the 4D case.

Findings

Exact LKFT solution in Minkowski space

Simplification of LKFT in 4D via fractional calculus

Verification of gauge dependence in 3D case

Abstract

We explore the dependence of fermion propagators on the covariant gauge fixing parameter in quantum electrodynamics (QED) with the number of spacetime dimensions kept explicit. Gauge covariance is controlled by the the Landau-Khalatnikov-Fradkin transformation (LKFT). Utilizing its group nature, the LKFT for a fermion propagator in Minkowski space is solved exactly. The special scenario of 3D is used to test claims made for general cases. When renormalized correctly, a simplification of the LKFT in 4D has been achieved with the help of fractional calculus.