# Gravitational dressing, soft charges, and perturbative gravitational splitting

## TL;DR

This paper explores how gauge-invariant operators in gravity and gauge theories can be dressed to analyze the localization of quantum information, revealing that soft charges are not uniquely tied to matter distributions and can be manipulated through radiative configurations.

## Contribution

It introduces a method to construct dressed operators with soft charges independent of matter distribution details, facilitating localized descriptions in gauge theories and gravity.

## Key findings

- Soft charges are not uniquely determined by matter distributions.
- Dressing can be chosen to decouple asymptotic observables from distribution details.
- Proposes electromagnetic and gravitational splittings for subsystem localization.

## Abstract

In gauge theories and gravity, field variables are generally not gauge-invariant observables, but such observables may be constructed by "dressing" these or more general operators. Dressed operators create particles, together with their gauge or gravitational fields which typically extend to infinity. This raises an important question of how well quantum information can be localized; one version of this is the question of whether soft charges fully characterize a given localized charge or matter distribution. This paper finds expressions for the non-trivial soft charges of such dressed operators. However, a large amount of flexibility in the dressing indicates that the soft charges, and other asymptotic observables, are not inherently correlated with details of the charge or matter distribution. Instead, these asymptotic observables can be changed by adding a general radiative (source-free) field configuration to the original one. A dressing can be chosen, perturbatively, so that the asymptotic observables are independent of details of the distribution, besides its total electric or Poincar\'e charges. This provides an approach to describing localization of information in gauge theories or gravity, and thus subsystems, that avoids problems associated with nonlocality of operator subalgebras. Specifically, this construction suggests the notions of electromagnetic or gravitational splittings, which involve networks of Hilbert space embeddings in which the charges play an important role.