Gravitational dressing, soft charges, and perturbative gravitational splitting
Steven B. Giddings
*
Department of Physics, University of California, Santa Barbara, California 93106, USA
and CERN, Theory Department, 1 Esplande des Particules, Geneva 23, CH-1211, Switzerland
(Received 25 May 2019; published 3 December 2019)
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 typ ically 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 nontrivial 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 Hilb ert space embeddings in which the charges play
an important role.
DOI: 10.1103/PhysRevD.100.126001
I. INTRODUCTION
Quantum information has become an important theme in
current theoretical physics. However, 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 in fact drive at the heart of some
of the most challenging questions in physics: can informa-
tion 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?
A way to investigate these questions is through the study
of observables, which can create excitations of the Hilbert
space. Indeed, a careful way to look at subsystems in field
theory is to define them via commuting subalgebras of the
algebra of observables, associated to spacelike separated
regions.
1
But, while the field variables are basic observ-
ables in nongauge theories, the field variables are not
typically gauge invariant in gauge theory or gravity, hence
are not physical observables. 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. For example, soft
charges
2
have been proposed as an important characteristic
of asymptotic gauge and gravitational fields, and it has been
suggested that asymptotically measured soft charges carry a
*
giddings@ucsb.edu
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI. Funded by SCOAP
3
.
1
For treatment of field theory from this perspective, see [1]; for
this view of subsystems, see [2]. In this paper, “observables”
mean quantum observables, which ordinarily are described as
gauge-invariant self-adjoint operators on the Hilbert space. These
are semantically distinguished from “things that observers/
experimentalists observe,” though of course are related. One
can use the terminology “q-observable” for the former, in cases
where confusion might arise; for further discussion see e.g. [3].
2
See [4] for a review.
PHYSICAL REVIEW D 100, 126001 (2019)
2470-0010=2019=100(12)=126001(10) 126001-1 Published by the American Physical Society
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