Note on soft photons and Faddeev-Jackiw symplectic reduction of quantum electrodynamics in the eikonal limit

TL;DR

This paper compares soft photon models and Faddeev-Jackiw quantization in massless QED's eikonal limit, revealing that gauge potentials become pure gauges and brackets match, suggesting a deep connection between the approaches.

Contribution

It demonstrates the equivalence of gauge potentials and brackets in soft photon and Faddeev-Jackiw approaches, highlighting a potential link between the two methods in the eikonal limit.

Findings

Gauge potentials become pure gauges in both approaches

Faddeev-Jackiw brackets match soft quantum brackets

Localization of gauge fields in two-dimensional planes

Abstract

In this note, we go over the recent soft photon model and Faddeev-Jackiw quantization of the massless quantum electrodynamics in the eikonal limit to some extent. Throughout our readdressing, we observe that the gauge potentials in both approaches become pure gauges and the associated eikonal Faddeev-Jackiw quantum bracket matches with the soft quantum bracket. These observations and the fact that the gauge fields in two cases localize in two-dimensional plane (even if it is spatial in soft photon case and $1+1$-dimensional Minkowski in the eikonal case) imply that there might be an interesting relation between these two distinct perspectives.