Landau-Khalatnikov-Fradkin Transformations in Reduced Quantum Electrodynamics: Perturbative and Nonperturbative Dynamics of the Fermion Propagator

TL;DR

This paper analyzes Landau-Khalatnikov-Fradkin transformations in reduced QED, providing all-order gauge transformations for the fermion propagator, exploring perturbative and nonperturbative effects, and demonstrating gauge invariance of key physical quantities.

Contribution

It offers a comprehensive all-order gauge transformation framework in RQED, extending previous studies and connecting perturbative results with renormalization constraints.

Findings

Optimal gauge choice is ξ=1/3 for massless fermions.

Leading logarithmic contributions vanish at one-loop in this gauge.

Gauge invariance of fermion condensate and pole mass is confirmed.

Abstract

We present a comprehensive analysis of the Landau-Khalatnikov-Fradkin transformations for the charged fermion propagator in reduced quantum electrodynamics (RQED). Starting from the propagator in a reference gauge, we perform a gauge transformation to obtain its analytical expression valid to all orders in an arbitrary covariant gauge and also applicable in a nonperturbative context. This work complements and extends previous studies of quantum electrodynamics in various spacetime dimensions, for both massless and massive fermions. At the perturbative level, we expand the resulting expressions up to two-loop order for both massless and massive cases, and compare our results with those available in the literature wherever possible. We argue that the most suitable choice of the reference covariant gauge in RQED is $\xi=1/3$, as in this case the leading logarithmic contribution to the massless wave-function renormalization vanishes at one-loop order. This choice provides a direct connection between perturbation theory and the constraints imposed by multiplicative renormalizability on the massless fermion propagator. We also investigate the implications of the Landau-Khalatnikov-Fradkin transformations for the dynamically generated mass function of the fermion propagator. Finally, through numerical computation, we demonstrate that both the chiral fermion condensate and the fermion pole mass are gauge-invariant quantities.