Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

TL;DR

This paper develops a generalized quantum electrodynamics model in the Heisenberg picture to address one-loop divergences, ensuring stability, unitarity, and gauge invariance, and analyzing quantum fluctuations without conflicts.

Contribution

It introduces a covariant quantization approach in the Heisenberg picture for generalized electrodynamics, overcoming limitations of perturbative Maxwell theory.

Findings

Elimination of one-loop divergences in the model

Absence of anomalous magnetic moment and mass-shell singularity

Stable, unitary, gauge-invariant quantum framework

Abstract

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag's theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.