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.
Highlights
Quantum information has become an important theme in current theoretical physics
In the context of gauge theories and in particular gravity, there are various puzzles about how to describe it, and in particular its localization. These puzzles drive at the heart of some of the most challenging questions in physics: can information be localized in a black hole, and how does it escape? Or, is that information manifest, in some way, in the gravitational field surrounding the black hole? Is there a precisely equivalent description of physics in a region of spacetime in terms of variables outside the region, or at an asymptotic boundary, as in anti–de Sitter space? In typical quantum systems, a notion of localization of information, e.g., in quantum subsystems, is a basic concept that is prior to many others, such as entanglement, information transfer, and computational complexity; is that true in gravity?
This paper studies the form of the soft charges for these operators, for electromagnetism (EM) and for gravity
Summary
Quantum information has become an important theme in current theoretical physics. in the context of gauge theories and in particular gravity, there are various puzzles about how to describe it, and in particular its localization. One way to rectify this situation is to “dress” fields, or more general operators, to construct gauge-invariant observables Such dressed observables typically create a nontrivial gauge or gravitational field extending to infinity, indicating a basic kind of nonlocal behavior. This raises the question of how much information about a given charge or mass distribution in a region is accessible in the corresponding field that extends outside the region. This plausibly holds for matter in a black hole, suggesting that soft charges will not help with the problem of unitarity This construction provides a way of describing localization of information in gauge theory, and in gravity, at least at a perturbative level. While this construction is clear in the EM case, some puzzles remain in the gravitational case, and in particular the question of nonperturbative completion of this structure is an important one [16]
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