A first nonperturbative calculation in light-front QED for an arbitrary covariant gauge

TL;DR

This paper presents the first nonperturbative calculation in light-front QED within an arbitrary covariant gauge, demonstrating gauge invariance of the dressed-electron state and its anomalous magnetic moment.

Contribution

It introduces a gauge-invariant nonperturbative framework for light-front QED using Stueckelberg quantization and Pauli-Villars regularization, applied to compute the electron's magnetic moment.

Findings

Gauge independence of the anomalous magnetic moment result.

Successful construction of a nonperturbative light-front QED Hamiltonian.

Validation of gauge invariance in a nonperturbative setting.

Abstract

This work is the first check of gauge invariance for nonperturbative calculations in light-front QED. To quantize QED in an arbitrary covariant gauge, we use a light-front analog of the equal-time Stueckelberg quantization. Combined with a Pauli-Villars regularization, where massive, negative-metric photons and fermions are included in the Lagrangian, we are then able to construct the light-front QED Hamiltonian and the associated mass eigenvalue problem in a Fock-space representation. The formalism is applied to the dressed-electron state, with a Fock-space truncation to include at most one photon. From this eigenstate, we compute the anomalous magnetic moment. The result is found to be gauge independent, to an order in $\alpha$ consistent with the truncation.