A Unified Geometric Framework for Boundary Charges and Particle Dressings

TL;DR

The paper tackles how boundary charges and particle dressings arise in gauge theories by introducing a field-space connection-form $\varpi$, enabling a covariant horizontal variation ${\mathbb{d}}_H$ and a dressed, gauge-invariant formulation. This geometric framework yields Dirac-like dressings in electrodynamics and a symplectic structure in which gauge charges vanish while global charges persist as physical symmetries. It unifies boundary phenomena and dressing mechanisms, clarifies how boundaries interact with gauge freedom, and suggests powerful extensions to non-Abelian and non-perturbative regimes, including connections to known dressings and confinement ideas. The approach has potential to impact both boundary physics and non-perturbative gauge theory by providing a common, covariant foundation for charges and dressings.

Abstract

We provide a unified geometrical origin for both boundary charges and particle dressings, with a focus on electrodynamics. The method is furthermore generalizable to QCD and gravity, and can be extended to the non-perturbative domain.