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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Infalling ultra-faint dwarfs as emissaries of the Axiverse

Recent discoveries of ultra-faint dwarf galaxies (UFDs) infalling onto the Milky Way, namely Leo K & M at r ≃ 450 kpc, considerably strengthens the case that UFDs constitute a distinct galaxy class that is inherently smaller and fainter, and metal-poorer than the classical dwarf spheroidals (dSph). This distinction is at odds with the inherent continuity of galaxy halo masses formed under scale-free gravity for any standard dark-matter (DM) model. Here, we show that distinct galaxy classes do evolve in cosmological simulations of multiple light bosons representing the “Axiverse” proposal of string theory, where a discrete mass spectrum of axions is generically predicted to span many decades in mass. In this context, the observed UFD class we show corresponds to a relatively heavy boson of 3 × 10 −21 eV, including Leo K & M, whereas a lighter axion of 10 −22 eV comprises the bulk of DM in all larger galaxies including the dSphs. Although Leo M is larger in size than Leo K, we predict its velocity dispersion to be smaller ( ≃ 1.7 km/s) than that of Leo K ( ≃ 4.5 km/s) because of the inverse de Broglie scale dependence on momentum. This scenario can be definitively tested using millisecond pulsars close to the Galactic center, where the Compton frequencies of the heavy and light bosons imprint monotone timing residuals that may be detected by the Square Kilometre Array (SKA) on timescales of approximately one week and four months, respectively.

dark matter↗
DOE OSTI2020

The Sensitivity of Joint Inversions of Seismic and Geodynamic Data to Mantle Viscosity

Seismic tomography has revealed the existence of large-scale velocity heterogeneities in the mantle. The interpretation of seismic velocity anomalies in terms of temperature and chemical composition is nonunique. We use geodynamic observations including gravity, plate motions, dynamic topography, and excess ellipticity of the core-mantle boundary combined with seismic observations to investigate the thermo-chemical structure of the mantle through joint inversions. An outstanding issue, however, is the physical connection between mantle density anomalies and the surface geodynamic observations, which requires knowledge of the mantle viscosity structure. Here we perform joint inversions assuming different viscosity profiles and examine the dependence of the results on the viscosity. We first assume that mantle heterogeneity is due to thermal variations, which places a constraint on the relation between seismic velocity and density, and we subsequently relax the constraint to allow for potential nonthermal effects. In all of our joint inversions, a nonthermal origin of density anomalies is required to explain the geodynamic data, though the amount varies with the assumed viscosity structure. A common observation is a high-density chemical signal in the center of the large low-shear-velocity provinces at the base of the mantle resulting in a near neutral or slightly dense overall buoyancy there. Using the derived density models and their corresponding viscosity profiles, we also calculate instantaneous mantle flow fields. The predicted flow fields derived from joint inversions are generally similar but are quite different from flow fields using density models derived from a posteriori scaling of pure seismic tomography models.

58 GEOSCIENCES↗
DOE OSTI2021

Approximate Bacon-Shor code and holography

We explicitly construct a class of holographic quantum error correction codes with non-trivial centers in the code subalgebra. Specifically, we use the Bacon-Shor codes and perfect tensors to construct a gauge code (or a stabilizer code with gauge-fixing), which we call the holographic hybrid code. This code admits a local log-depth encoding/decoding circuit, and can be represented as a holographic tensor network which satisfies an analog of the Ryu-Takayanagi formula and reproduces features of the sub-region duality. We then construct approximate versions of the holographic hybrid codes by “skewing” the code subspace, where the size of skewing is analogous to the size of the gravitational constant in holography. These approximate hybrid codes are not necessarily stabilizer codes, but they can be expressed as the superposition of holographic tensor networks that are stabilizer codes. For such constructions, different logical states, representing different bulk matter content, can “back-react” on the emergent geometry, resembling a key feature of gravity. The locality of the bulk degrees of freedom becomes subspace-dependent and approximate. Such subspace-dependence is manifest from the point of view of the “entanglement wedge” and bulk operator reconstruction from the boundary. Exact complementary error correction breaks down for certain bipartition of the boundary degrees of freedom; however, a limited, state-dependent form is preserved for particular subspaces. We also construct an example where the connected two-point correlation functions can have a power-law decay. Coupled with known constraints from holography, a weakly back-reacting bulk also forces these skewed tensor network models to the “large N limit” where they are built by concatenating a large N number of copies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Constraints on long-range forces in de Sitter space

The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

AdS-CFT Correspondence↗
DOE OSTI2021

Opportunities for DOE National Laboratory-led QuantISED Experiments

A subset of QuantISED Sensor PIs met virtually on May 26, 2020 to discuss a response to a charge by the DOE Office of High Energy Physics. In this document, we summarize the QuantISED sensor community discussion, including a consideration of HEP science enabled by quantum sensors, describing the distinction between Quantum 1.0 and Quantum 2.0, and discussing synergies/complementarity with the new DOE NQI centers and with research supported by other SC offices. Quantum 2.0 advances in sensor technology offer many opportunities and new approaches for HEP experiments. The DOE HEP QuantISED program could support a portfolio of small experiments based on these advances. QuantISED experiments could use sensor technologies that exemplify Quantum 2.0 breakthroughs. They would strive to achieve new HEP science results, while possibly spinning off other domain science applications or serving as pathfinders for future HEP science targets. QuantISED experiments should be led by a DOE laboratory, to take advantage of laboratory technical resources, infrastructure, and expertise in the safe and efficient construction, operation, and review of experiments. The QuantISED PIs emphasized that the quest for HEP science results under the QuantISED program is distinct from the ongoing DOE HEP programs on the energy, intensity, and cosmic frontiers. There is robust evidence for the existence of particles and phenomena beyond the Standard Model, including dark matter, dark energy, quantum gravity, and new physics responsible for neutrino masses, cosmic inflation, and the cosmic preference for matter over antimatter. Where is this physics and how do we find it? The QuantISED program can exploit new capabilities provided by quantum technology to probe these kinds of science questions in new ways and over a broader range of science parameters than can be achieved with conventional techniques.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Space Mission Options for Reconnaissance and Mitigation of Asteroid 2024 YR4

Near-Earth asteroid 2024 YR 4 was discovered on 2024-12-27 and its probability of Earth impact in December 2032 peaked at ~3% on 2025-02-18. Additional observations ruled out Earth impact by 2025-02-23. However, the probability of lunar impact in December 2032 then rose, reaching ~4% by the end of the apparition in May 2025. James Webb Space Telescope (JWST) observations on 2025-03-26 estimated the asteroid’s diameter at 60 ± 7 m. Studies of 2024 YR 4 ’s potential lunar impact effects suggest lunar ejecta could increase micrometeoroid debris flux in low Earth orbit up to 1000 times above background levels over just a few days, possibly threatening astronauts and spacecraft. In this work, we present options for space missions to 2024 YR 4 that could be utilized if lunar impact is confirmed. Here, we cover flyby & rendezvous reconnaissance, deflection, and robust disruption of the asteroid. We examine both rapid-response and delayed launch options through 2032. We evaluate chemical and solar electric propulsion, various launch vehicles, optimized deep space maneuvers, and gravity assists. Re-tasking extant spacecraft and using built spacecraft not yet launched are also considered. The best reconnaissance mission options launch in late 2028, leaving only approximately three years for development at the time of this writing in August 2025. Deflection missions were assessed and appear impractical. However, kinetic robust disruption missions are available with launches between April 2030 and April 2032. Nuclear robust disruption missions are also available with launches between late 2029 and late 2031. Finally, even if lunar impact is ruled out there is significant potential utility in deploying a reconnaissance mission to characterize the asteroid.

Asteroid deflection↗
DOE OSTI2020

Utah FORGE: Phase 3 Magnetotelluric (MT) Data

New high-quality tensor MT data at 122 sites, including the vertical magnetic field and utilizing ultra-remote referencing, have been acquired over the Utah FORGE project area. The results will be used to delineate the densities of faults and fractures in crystalline basement rocks, to define the heat sources, and to derive baseline 3D resistivity structure for later MT monitoring of temporal changes in resistivity structure following well stimulation in the EGS reservoir. There are three files here related to Utah FORGE magnetotelluric (MT) data acquisition and processing. The FORGE MT EDIs zip file contains the observed MT responses in industry-standard EDI format. For each site, there is an EDI response file that utilized a local independent reference for noise cancellation, and a file that utilized a distant reference cancelling noise associated with the DC transmission line of the Delta IPP passing down the west side of Milford Valley. These two site files could be merged as appropriate. The FORGE Model Cell Center file contains the model volume of the 3D Forge MT inversion for characterizing the resistivity structure in the project area. It was derived using finite element inversion methodology described in Wannamaker et al, in the attached FORGE Phase3 Geophysics paper, from the MT observation EDI files. It is ASCII format (.dat) and entries are defined at top of the file in a simple x-y-z-Rho listing in UTM coordinates. The element layers drape the topography so the Rho value layers are not purely horizontal slices. This greatly simplifies the listing.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Particle dynamics and geometric optics in Chern–Simons black holes

Highlights: • Black holes in Chern–Simons modified gravity have been studied. • The effects of the coupling constant of the Chern–Simons gravity on some physical quantities have been investigated. • The dependence of Hawking mass and Penrose process on the coupling constant is studied. • Rotation of the polarization vector is also studied for dependence on the Chern–Simons coupling constant. In this paper we study the effects of the coupling constant of the Chern–Simons modified gravity on some physical properties of black holes. The Hawking mass is one of the proposed definitions of quasilocal mass. We find that, for slowly rotating Chern–Simons black holes, the Hawking mass is independent of the coupling constant. Next, we show the dependence on the centre of mass energy, for two neutral colliding particles, of coupling constant and the rotation parameter. We also investigate energy extraction through Penrose process and find that the energy gain and efficiency of the Penrose process are independent of this coupling constant. Rotation of the polarization vector is also studied for dependence on the Chern–Simons coupling constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Evidence for an Early Formation of Serenitatis Basin at 4.25 Ga Shifts Lunar Chronology

Troctolite sample 76535, collected in Serenitatis basin during Apollo 17, formed at least 50 km deep, experienced maximum shock pressures of 6 GPa, and has a 40 Ar/ 39 Ar excavation age of 4.25 Ga. Previous work attributed 76535 to the South Pole-Aitken (SPA) basin, presumably dating the SPA-impact and constraining lunar bombardment history. Here we use the iSALE-2D shock-physics code and gravity inversion modeling to determine if instead the Serenitatis impact event excavated 76535. We find nearly 140,000 km 3 of material (∼2% of near-surface ejecta) matching the depth and pressure constraints of 76535 is displaced to the surface during crater collapse of a Serenitatis-like impact event. We conclude that the Serenitatis impact event possibly excavated 76535, redefining its age to 4.25 Ga, 300 My older than the consensus age based on Apollo 17 samples. This finding would provide an important anchor point where lunar chronology where bombardment flux is especially uncertain.

Bjonnes, Evan [Lawrence Livermore National Laborat↗
DOE OSTI2023

Energy cost of localization of relational quantum information

Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes to localize the quantum information within a spatially separated entangled state, one must enact an entanglement extraction protocol also defined with respect to that external frame. Entanglement extraction for Gaussian ground states in such an external frame construction has been shown to require a minimum energy and is hence an interesting process for gravitational physics, where examinations of localization vs energy cost have a long history. General covariance, however, precludes dependence on external frames. In order to enact an extraction protocol in a generally covariant theory, dependence on the external reference frame must first be removed and the states made relational. Here, we examine the implementation of an extraction protocol for Gaussian states, whose center of mass and relational degrees of freedom are entangled, in a relational toy model where translation invariance stands in for full diffeomorphism invariance. Constructing fully relational states and the corresponding extraction/localization can, in principle, be done in two ways. External frame position information can be removed through 𝐺-twirling over translations or one can spontaneously break the translation symmetry via the gradient of an auxiliary field, or 𝑍-model. We determine the energetics of quantum information localization after the states have been made fully relational via both the 𝐺-twirl and 𝑍-model. We also show one can obtain the 𝐺-twirl construction from a 𝑍-model as a limit of positive operator valued measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Strong gravity extruding peaks in speed of sound profiles of massive neutron stars

The speed of sound squared (SSS) s 2 in massive neutron stars (NSs) characterizes not only the stiffness of supradense neutron-rich matter within but also equivalently properties of the curved geometry due to the strong-field gravity and matter-geometry coupling. A peaked density or radius profile of s 2 has been predicted for massive NSs using various NS equation of state (EOS) models. However, the nature, cause, location and size of the peak in s 2 profiles are still very EOS model dependent. In this work, we investigate systematically s 2 profiles in massive NSs in a new approach that is independent of the nuclear EOS model and without any presumption about the NS structure and/or composition. In terms of the small quantities (reduced radius, the energy density and pressure scaled by their central values), we perform double-element perturbative expansions in solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations and analyzing s 2 profiles from the Newtonian limit to the general relativistic (GR) case. The GR term in the TOV equations plays a twofold role: it compresses NS matter and modifies the pressure/energy density ratio from small values in Newtonian stars showing no s 2 peak to large ones for massive NSs possessing a peak in their s 2 profiles, and eventually takes away the peak in extremely compact/massive NSs approaching the causality limit. In particular, the peaked behavior in s 2 is expected to emerge near the center of massive NSs like PSR J⁢0740+6620, while a sharp phase transition is unlikely to occur there. Furthermore, these features revealed from our analyses are universal as they are intrinsic properties of the GR stellar structure equations independent of the still very uncertain EOS of supradense neutron-rich matter in NSs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Self-consistent interaction of linear gravitational and electromagnetic waves in non-magnetized plasma

Here, this paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (“oscillation-center”) Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for $longitudinal$ GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Searching for ultra-light bosons and constraining black hole spin distributions with stellar tidal disruption events

Stars that pass close to the supermassive black holes located in the center of galaxies can be disrupted by tidal forces, leading to flares that are observed as bright transient events in sky surveys. The rate for these events to occur depends on the black hole spins, which in turn can be affected by ultra-light bosons due to superradiance. We perform a detailed analysis of these effects and show that searches for stellar tidal disruptions have the potential to uncover the existence of ultra-light bosons. In particular, we find that upcoming stellar tidal disruption rate measurements by the Vera Rubin Observatory’s Legacy Survey of Space and Time can be used to either discover or rule out bosons with masses ranging from 10 –20 to 10 –18 eV. Our analysis also indicates that these measurements may be used to constrain a variety of supermassive black hole spin distributions and determine if close-to maximal spins are preferred.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Large-d phase transitions in holographic mutual information

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in G N in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large- d , we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large- d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large- d expansion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗
DOE OSTI2025

The Energy Exascale Earth System Model Version 3: 1. Overview of the Atmospheric Component

This paper describes the atmospheric component of the US Department of Energy's Energy Exascale Earth System Model (E3SM) version 3. Significant updates have been made to the atmospheric physics compared to earlier versions. Specifically, interactive gas chemistry has been implemented, along with improved representations of aerosols and dust emissions. A new stratiform cloud microphysics scheme more physically treats ice processes and aerosol‐cloud interactions. The deep convection parameterization has been largely improved with sophisticated microphysics for convective clouds, making model convection sensitive to large‐scale dynamics, and incorporating the dynamical and physical effects of organized mesoscale convection. Improvements in aerosol wet removal processes and parameter re‐tuning of key aerosol and cloud processes have improved model aerosol radiative forcing. The model's vertical resolution has increased from 72 to 80 layers with the extra eight layers added in the lower stratosphere to better simulate the Quasi‐Biennial Oscillation. These improvements have enhanced E3SM's capability to couple aerosol, chemistry, and biogeochemistry and reduced some long‐standing biases in simulating tropical variability. Compared to its predecessors, the model shows a much stronger signal for the Madden‐Julian Oscillation, Kelvin waves, mixed Rossby‐gravity waves, and eastward inertia‐gravity waves. Aerosol radiative forcing has been considerably reduced and is now better aligned with community best estimates, leading to significantly improved skill in simulating historical temperature records. Its simulated mean‐state climate is largely comparable to E3SMv2, but with some notable degradation in shortwave cloud radiative effect, precipitable water, and surface wind stress, which will be addressed in future updates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order

We compute the conservative and radiation-reaction contributions to classical observables in the gravitational scattering between a spinning and a spinless black hole to the fourth order in spin and third order in the gravitational constant. The conservative results are obtained from two-loop amplitudes for the scattering process of a massive scalar with a massive spin-𝑠 field (𝑠=0, 1, 2) minimally coupled to gravity, employing the recently introduced spin interpolation method to resolve all spin-Casimir terms. The two-loop amplitude exhibits a spin-shift symmetry in both probe limits, which we conjecture to be a sign of yet unknown integrability of Kerr orbits through the quartic order in spin and to all orders in the gravitational constant. We obtain the radial action from the finite part of the amplitude and use it to compute classical observables, including the impulse and spin kick. This is done using the recently introduced covariant Dirac brackets, which allow for the computation of classical scattering observables for general (nonaligned) spin configurations. Finally, employing the radiation-reaction amplitude proposed by Alessio and Di Vecchia, together with the Dirac brackets, we obtain radiation-reaction contributions to observables at all orders in spin and beyond the aligned-spin limit. We find agreement with known results up to the quadratic order in spin for both conservative and radiation-reaction contributions. Our results advance the state of the art in the understanding of spinning binary dynamics in general relativity and demonstrate the power and simplicity of the Dirac bracket formalism for relating scattering amplitudes to classical observables.

general relativity↗