arXiv subjects

Josh Kirklin

Publications and source records attributed to Josh Kirklin.

16 recordsLinked to original sources

arXiv2026

Gravitational null rays: Covariant Quantization and the Dressing Time

We quantize the degrees of freedom on a gravitational null ray segment in a fully gauge-invariant manner by using the dressing time as a quantum reference frame (QRF). Our work goes beyond previous models in that the QRF we employ is made out of the gravitational field itself, and accounts for the full group of diffeomorphisms along the ray, not just a locally compact subgroup. The key tool we introduce is covariant normal ordering, a QRF-dependent but background-independent renormalization prescription that restores diffeomorphism covariance at the quantum level. This enables the definition of a quantum dressing map whose image is the algebra of gauge-invariant observables. We find that this algebra carries the structure of a Virasoro crossed product, and that the dressing map induces a deformed product on gauge-fixed operators which can be understood as a quantization of the Dirac bracket, with consequences for the fluctuations of observables. We explain how to cancel anomalies in the physical Hilbert space representation of the gauge-invariant algebra by including a deformation at the classical level, thereby eliminating all spurious degrees of freedom at the quantum level. The physical Hilbert space admits a Page-Wootters reduction map to the perspective of the dressing time, and we show that the dressing time is non-ideal in the sense that its distinct coherent states have non-vanishing overlaps governed by the Teo-Takhtajan energy, i.e. the K\"ahler potential for Virasoro coadjoint orbits.

hep-th↗

arXiv2025

Fighting non-locality with non-locality: microcausality and boundary conditions in QED

In gauge theories, globally charged observables necessarily depend non-locally on the kinematical fields, with this dependence extending to the asymptotic boundary of spacetime. Despite this, we show that a subset of such observables can be consistently regarded as local to the bulk, in a manner that respects microcausality and leaves locality properties of uncharged observables untouched. A sufficient condition for this is to impose kinematically non-local boundary conditions on the large gauge sector of the theory, and to invoke a relational notion of localisation for observables. This reveals a relatively underappreciated link between boundary conditions, and different notions of microcausality and locality. We develop this point through a detailed case study in scalar QED, describing non-local boundary conditions that allow a large family of observables on a codimension-1 bulk surface to be viewed as local to that surface, despite being dressed by asymptotic Wilson lines. We show that this property continues to hold within a perturbative quantisation of the theory, and we argue that this leads to a consistent local net of algebras that includes these charged observables in bulk algebras. We explain how this setup may be understood in terms of a preferred dynamical reference frame for small gauge transformations appearing in the boundary conditions. Many features of the theory (such as microcausality, the vacuum state, and the net of algebras of observables) depend on the choice of this frame, and we briefly discuss some repercussions of this for algebraic formulations of QFT. While our analysis is performed in QED, we expect our results to carry over qualitatively to more complicated theories including gravity.

hep-th↗

arXiv2025

Localization and anomalous reference frames in gravity

In this work, we study the classical phase space for the gravitational degrees of freedom along a null ray. We construct gauge-invariant observables localized on a null ray segment that commute with those localized on the complement; thus, the phase space describes a genuine gravitational subsystem compatible with both locality and diffeomorphism invariance. Our construction employs 'dressing time' (a null time coordinate built from spin 0 gravitational degrees of freedom) as a dynamical reference frame. The existence of such a frame depends on the use of edge mode variables, which we argue are generally required to upgrade a local gauge-fixing condition to a global 'frame-fixing'. To analyze the effects of quantum diffeomorphism anomalies on these structures, we then establish an 'effective' classical description in which the Raychaudhuri equation, symplectic form, and edge mode variables all acquire Virasoro-type deformations. Within this framework, we identify three distinct diffeomorphism actions: reparametrizations (gauge transformations), reorientations (physical symmetries of the reference frame), and dressed reparametrizations. Each acquires its own central extension and plays a different crucial role in the effective theory. The resulting structures provide a foundation for quantizing gravitational null ray segments, including promoting dressing time to a genuine quantum reference frame.

hep-th↗

arXiv2024

Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy

A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III algebra of QFT observables in a gravitational subregion to a Type II crossed product, whose entropy reduces to the generalized entropy formula in a semiclassical limit. The observers thus used are also known as quantum reference frames (QRFs); as noted in our companion work [arXiv:2405.00114], using different QRFs result in different algebras, and hence different entropies -- so gravitational entropy is observer-dependent. Here, we provide an in-depth analysis of this phenomenon, with full derivations of many new results. Using the perspective-neutral QRF formalism, we extend previous constructions to allow for arbitrarily many observers, each carrying a clock with possibly degenerate energy spectra. We consider a semiclassical regime characterized by clocks whose energy fluctuations dominate over the fluctuations of the energy of the QFT. Unlike previous works, we allow the clocks and fields to be arbitrarily entangled. At leading order the von Neumann entropy still reduces to the generalized entropy, but linear corrections are typically non-vanishing and quantify the degree of entanglement between the clocks and fields. We also describe an `antisemiclassical' regime as the opposite of the semiclassical one, with suppressed fluctuations of the clock energy; in this regime, we show how the clock may simply be `partially traced' out when evaluating the entropy. Four explicit examples of observer-dependent entropy are then given, involving a gravitational interferometer, degenerate clock superselection, a semiclassical approximation applying to some clocks but not others, and differences between monotonic and periodic clocks.

hep-th↗

arXiv2024

Generalised second law beyond the semiclassical regime

We prove that the generalised second law (GSL), with an appropriate modification, holds in perturbative gravity to all orders beyond the semiclassical limit and without a UV cutoff imposed on the fields. Our proof uses algebraic techniques and builds on the recent work of Faulkner and Speranza, which combined Wall's proof of the GSL with the identification of generalised entropy as the von Neumann entropy of a boost-invariant crossed product algebra. The key additional step in our approach is to further impose invariance under null translations. Doing so requires one to describe horizon exterior regions in a relational manner, so we introduce `dynamical cuts': quantum reference frames which give the location of a cut of the horizon. We use idealised dynamical cuts, but expect that our methods can be generalised to more realistic models. The modified GSL that we prove says that the difference in generalised entropies of the regions outside two dynamical cuts is bounded below by the free energy of the degrees of freedom giving the location of the later cut. If one takes a semiclassical limit, imposes a UV cutoff, and requires the cuts to obey certain energy conditions, then our result reduces to the standard GSL.

hep-th↗

arXiv2024

Linearization (in)stabilities and crossed products

Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain boost constraints on gravitons, QRFs and other fields. Here, we revisit the question of how these constraints should be understood through the lens of perturbation theory and particularly the study of linearization (in)stabilities, exploring when linearized solutions can be integrated to exact ones. Our aim is to provide some clarity about the status of justification, under various conditions, for imposing such constraints on the linearized theory in the $G_N\to0$ limit as they turn out to be of second-order. While for spatially closed spacetimes there is an essentially unambiguous justification, in the presence of boundaries or the absence of isometries this depends on whether one is also interested in second-order observables. Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations and to address this in a unified framework, we translate the subject from the usual canonical formulation into a systematic covariant phase space language. This overcomes theory-specific arguments, exhibiting the universal structure behind (in)stabilities, and permits us to cover arbitrary generally covariant theories. We comment on the relation to modular flow and illustrate our findings in several gravity and gauge theory examples.

hep-th↗

arXiv2024

Gravitational entropy is observer-dependent

In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers and for arbitrary global physical states), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the `observers' considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. [arXiv:2206.10780] is equivalent to the Page-Wootters formalism, leading to the informal slogan "PW=CLPW". It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.

hep-th↗

arXiv2023

Probes, purviews, purgatories, parable, paradox?

I discuss some general information-theoretic properties of quantum mechanical probes in semiclassical gravity: their purview, i.e. what they can see and act on (in terms of a generalised entanglement wedge), their spontaneous evaporation into a cloud of highly entropic particles when one tries to make them see too much (perhaps a parable on the dangers of straining one's eyes), and the subsequent resolution of an apparent information paradox.

hep-th↗

arXiv2022

Emergent classical gauge symmetry from quantum entanglement

We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterisation of when it is consistent to treat a quantum subsystem classically in such a limit, namely: in any quantum state corresponding to a definite classical state in the classical limit, the reduced density matrix of the subsystem must be approximately proportional to a projection operator, and the projection operators for different classical subsystem states must obey an approximate mutual orthogonality condition. These are strong constraints on the entanglement structure of classical states. They generically give rise to fundamentally non-local classical degrees of freedom, which may nevertheless be accounted for using a completely local kinematical description, if one gauges this description in the right way. The mechanism we describe is very general, but for concreteness we exhibit a toy example involving three entangled spins at high angular momentum, and we also describe a significant group-theoretic generalisation of this toy example. Finally, we give evidence that this phenomenon plays a role in the emergence of bulk diffeomorphism invariance in gravity.

hep-th↗

arXiv2022

Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance

We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use of a 'universal dressing space', which contains as a subset every possible dynamical frame. We describe examples of such frames, including matter frames, a popular construction based on boundary-anchored geodesics and one using minimal surfaces -- but our formalism does not depend on the existence of a boundary. The class of observables we construct generalises and unifies the dressed and relational approaches to constructing gravitational observables, including single-integral and canonical power-series constructions. All these (possibly gravitationally charged) relational observables describe physics in a precise sense relative to the dynamical frame and respect a notion of 'relational' locality based on the relationships between fields. By using 'relational atlases', i.e. collections of dynamical frames glued together by field-dependent maps (which are relational observables too), we can construct relationally local observables throughout spacetime. This further establishes a framework for dynamical frame covariance that permits us to change between arbitrary relational frame perspectives. Relational locality obeys many desirable properties: we prove that it satisfies microcausality in the bulk (in tension with previous work done mainly in a perturbative setting which we comment on), and show that it permits a relational version of local bulk dynamics. Relational locality is therefore arguably more physically meaningful than the ordinary notion of locality. Thus, our formalism -- which we argue to be an updated, gauge-invariant version of general covariance -- refutes the commonly claimed non-existence of local gravitational bulk physics.

hep-th↗

arXiv2020

Islands and Uhlmann phase: Explicit recovery of classical information from evaporating black holes

Recent work has established a route towards the semiclassical validity of the Page curve, and so provided evidence that information escapes an evaporating black hole. However, a protocol to explicitly recover and make practical use of that information in the classical limit has not yet been given. In this paper, we describe such a protocol, showing that an observer may reconstruct the phase space of the black hole interior by measuring the Uhlmann phase of the Hawking radiation. The process of black hole formation and evaporation provides an invertible map between this phase space and the space of initial matter configurations. Thus, all classical information is explicitly recovered. We assume in this paper that replica wormholes contribute to the gravitational path integral.

hep-th↗

arXiv2020

Holography from Decoherence and Entanglement

We describe an explicit mechanism for the emergence of a dynamical holographic bulk from the structure of entanglement in a quantum state. We start with a generic system in complete isolation, assuming it has a classical limit involving coherent states. Then we entangle it with another system of that kind, and subject the pair to a decohering process. We make a number of broadly applicable and physically reasonable assumptions about this setup. First, we assume that the states selected by the decoherence (called pointer states) have the same local symmetries as the isolated systems, in a sense which is made precise. We also assume that the modular Hamiltonians of pointer states scale inversely with Planck's constant, so that the pointer states are highly entangled in the classical limit. Finally, we require the timescale of decoherence to scale in a certain way with Planck's constant, so that decoherence happens very frequently in the classical limit, but not too frequently. Given these assumptions, we demonstrate that the semiclassical evolution of the system is dominated by a certain dynamical generalisation of Uhlmann holonomy. We construct a coherent state path integral for this evolution, showing that the semiclassical fields evolve in a spacetime with one more dimension than the isolated case. The additional dimension is generated by modular flow.

hep-th↗

arXiv2019

The Holographic Dual of the Entanglement Wedge Symplectic Form

In this paper, we find the boundary dual of the symplectic form for the bulk fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which is a notion of parallel transport of purifications of density matrices based on a maximisation of transition probabilities. Using a replica trick, we compute this holonomy for curves of reduced states in boundary subregions of holographic QFTs at large N, subject to changes of operator insertions on the boundary. It is shown that the Berry phase along Uhlmann parallel paths may be written as the integral of an abelian connection whose curvature is the symplectic form of the entanglement wedge. This generalises previous work on holographic Berry curvature.

hep-th↗

arXiv2019

Unambiguous Phase Spaces for Subregions

The covariant phase space technique is a powerful formalism for understanding the Hamiltonian description of covariant field theories. However, applications of this technique to problems involving subregions, such as the exterior of a black hole, have heretofore been plagued by boundary ambiguities. We provide a resolution of these ambiguities by directly computing the symplectic structure from the path integral, showing that it may be written as a contour integral around a partial Cauchy surface. This result has implications for gauge symmetry and entanglement.

hep-th↗

arXiv2018

Subregions, Minimal Surfaces, and Entropy in Semiclassical Gravity

For a large class of density matrices in semiclassical gravity, it is shown that the reduced density matrix which corresponds to tracing over the degrees of freedom in a spatial subregion is dominated by states for which the area of the boundary of the subregion is minimised. In the semiclassical limit, the entropy of the reduced density matrix is found to have a leading order contribution equal to one quarter of the minimal area in natural units. This is consistent with the Ryu-Takayanagi conjecture. An extension to higher derivative theories of gravity is established, for which the area is replaced by a dynamical generalisation of the Wald entropy.

hep-th↗

arXiv2018

Localisation of Soft Charges, and Thermodynamics of Softly Hairy Black Holes

Large gauge transformations (LGT) in asymptotically flat space are generated by charges defined at asymptotic infinity. No method for unambiguously localising these charges into the interior of spacetime has previously been established. We determine what this method must be, and use it to find localised expressions for the LGT charges. Applying the same principle to the case of a charged black hole spacetime leads to angle-dependent generalisations of the Smarr formula and the first law of black hole mechanics, both of which have important thermodynamical implications. In particular, the presence of a heat current intrinsic to the event horizon is observed.

hep-th↗