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DOE OSTI2021

Excited-State Dynamics and Nonlinear Optical Properties of Hyperpolarizable Chromophores Based on Conjugated Bis(terpyridyl)Ru(II) and Palladium and Platinum Porphyrinic Components: Impact of Heavy Metals upon Supermolecular Electro-Optic Properties

A new series of strongly coupled oscillators based upon (porphinato)Pd, (porphinato)Pt, and bis(terpyridyl)-ruthenium(II) building blocks is described. These RuPPd, RuPPt, RuPPdRu, and RuPPtRu chromophores feature bis- (terpyridyl)Ru(II) moieties connected to the (porphinato)metal unit via an ethyne linker that bridges the 4!-terpyridyl and porphyrin macrocycle meso-carbon positions. Pump–probe transient optical data demonstrate sub-picosecond excited singlet-to-triplet-state relaxation. The relaxed lowest-energy triplet (T 1 ) excited states of these chromophores feature absorption manifolds that span the 800–1200 nm spectral region, microsecond triplet-state lifetimes, and large absorptive extinction coefficients [ε(T 1 → T n ) > 4 × 10 4 M –1 cm –1 ]. Dynamic hyperpolarizability (β λ ) values were determined from hyper-Rayleigh light scattering (HRS) measurements carried out at several incident irradiation wavelengths over the 800–1500 nm spectral region. Relative to benchmark RuPZn and RuPZnRu chromophores which showed large βHRS values over the 1200–1600 nm range, RuPPd, RuPPt, RuPPdRu, and RuPPtRu displayed large βHRS values over the 850–1200 nm region. Generalized Thomas–Kuhn sum (TKS) rules and experimental hyperpolarizability values were utilized to determine excited state-to-excited state transition dipole terms from experimental electronic absorption data and thus assessed frequency-dependent β λ values, including two- and three-level contributions for both β zzz and β xzx tensor components to the RuPPd, RuPPt, RuPPdRu, and RuPPtRu hyperpolarizability spectra. Furthermore, these analyses qualitatively rationalize how the βzzz and βxzx tensor elements influence the observed irradiation wavelength-dependent hyperpolarizability magnitudes. The TKS analysis suggests that supermolecules related to RuPPd, RuPPt, RuPPdRu, and RuPPtRu will likely feature intricate dependences of experimentally determined βHRS values as a function of irradiation wavelength that derive from substantial singlet–triplet mixing, and complex interactions among multiple different β tensor components that modulate the long wavelength regime of the nonlinear optical response.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Hunting extreme BL Lacertae blazars with Fermi-Large Area Telescope

ABSTRACT The emission of very-high-energy (VHE) photons ($E\ \gt\ 100\ \mathrm{GeV}$) in blazars is closely connected to the production of ultra-relativistic particles and the role of these γ-ray sources as cosmic particle accelerators. This work focuses on a selection of 22 γ-ray objects from the 2BIGB catalogue of high-synchrotron-peaked sources, which are classified as blazar candidates of uncertain type in the 4FGL-DR2 catalogue. We study these sources by means of a re-analysis of the first 10 yr of γ-ray data taken with the Fermi-Large Area Telescope, including the attenuation by the extragalactic background light. Their broad-band spectral energy distributions are also evaluated, using multiwavelength archival data in the radio, optical, and X-ray bands, in terms of one-zone synchrotron-self-Compton models, adding an external Compton component when needed. Out of this analysis, we identify 17 new extreme high-synchrotron-peaked (EHSP) candidates and compare their physical parameters with those of prototypical EHSP blazars. Finally, the resulting models are used to assess their detectability by the present and future generation of ground-based Imaging Atmospheric Cherenkov Telescopes. We find two VHE candidates within the reach of the current and next generation of Cherenkov telescopes: J0847.0−2336 and J1714.0−2029.

Nievas Rosillo, M. (ORCID:0000000283219168)↗

DOE OSTI2023

Ageing and quenching through the Ageing Diagram – II. Physical characterization of galaxies

The connection between quenching mechanisms, which rapidly turn star-forming systems into quiescent, and the properties of the galaxy population remains difficult to discern. In this work we investigate the physical properties of MaNGA and SAMI galaxies at different stages of their star formation history. Specifically, we compare galaxies with signatures of recent quenching (Quenched) – Hα in absorption and low D n (4000) – with the rest of the low star-forming and active population (Retired and Ageing, respectively). The analysis is performed in terms of characteristics such as the total stellar mass, half-light radius, velocity-to-dispersion ratio, metallicity, and environment. We find that the Ageing population comprises a heterogeneous mixture of galaxies, preferentially late-type systems, with diverse physical properties. Retired galaxies, formerly Ageing or Quenched systems, are dominated by early-type high-mass galaxies found both at low and dense environments. Most importantly, we find that recently quenched galaxies are consistent with a population of compact low-mass satellite systems, with higher metallicities than their Ageing analogues. We argue that this is compatible with being quenched after undergoing a star-burst phase induced by environmental processes (e.g. ram pressure). However, we also detect a non-negligible fraction of field central galaxies likely quenched by internal processes. This study highlights that, in order to constrain the mechanisms driving galaxy evolution, it is crucial to distinguish between old (Retired) and recently quenched galaxies, thus requiring at least two estimates of the specific star formation rate over different time-scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Dual-Responsive Turn-On T 1 Imaging-Guided Mild Photothermia for Precise Apoptotic Cancer Therapy

Apoptosis has gained increasing attention in cancer therapy as an intrinsic signaling pathway, which leads to minimal leakage of waste products from a dying cell to neighboring normal cells. Among various stimuli to trigger apoptosis, mild hyperthermia is attractive but confronts limitations of non-specific heating and acquired resistance from elevated expression of heat shock proteins. Here, a dual-stimulation activated turn-on T 1 imaging-based nanoparticulate system (DAS) is developed for mild photothermia (≈43 °C)-mediated precise apoptotic cancer therapy. In the DAS, a superparamagnetic quencher (ferroferric oxide nanoparticles, Fe 3 O 4 NPs) and a paramagnetic enhancer (Gd-DOTA complexes) are connected via the N6-methyladenine (m 6 A)-caged, Zn 2+ -dependent DNAzyme molecular device. The substrate strand of the DNAzyme contains one segment of Gd-DOTA complex-labeled sequence and another one of HSP70 antisense oligonucleotide. When the DAS is taken up by cancer cells, overexpressed fat mass and obesity-associated protein (FTO) specifically demethylates the m 6</-sup>A group, thereby activating DNAzymes to cleave the substrate strand and simultaneously releasing Gd-DOTA complex-labeled oligonucleotides. The restored T 1 signal from the liberated Gd-DOTA complexes lights up the tumor to guide the location and time of deploying 808 nm laser irradiation. Afterward, locally generated mild photothermia works in concert with HSP70 antisense oligonucleotides to promote apoptosis of tumor cells. This highly integrated design provides an alternative strategy for mild hyperthermia-mediated precise apoptotic cancer therapy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

The ion-gas-neutral interactions with surfaces-2 (IGNIS-2) facility for the study of plasma–material interactions

The Ion-Gas-Neutral Interactions with Surfaces-2 (IGNIS-2) surface science facility has been designed at the Pennsylvania State University with the specific purpose of enabling experiments to study plasma–material interactions. This in situ surface modification and characterization facility consists of multiple reconfigurable substations that are connected through a central transfer chamber. This fully connected vacuum system ensures that the physical and chemical properties of samples are not altered between surface modification and analysis. The modification techniques in IGNIS-2 include a low-energy (<300 eV), high-flux (up to 1016 cm−2 s−1) broad-beam ion source, a liquid metal dropper, a lithium injection system, an RF sputter source, and an evaporator. Its characterization techniques include charged particle-based techniques, such as low-energy ion scattering (enabled by two <5 keV ion sources) and x-ray photoelectron spectroscopy, and photon and light-based techniques, such as x-ray fluorescence, multi-beam optical stress sensors, and optical cameras. All of these techniques can be utilized up to mTorr pressures, allowing both in situ and in operando studies to be conducted. Results are presented on lithium wetting experiments of argon-irradiated tungsten-based composites, surface stress measurements of tungsten films during deuterium ion irradiation, and temperature-programmed desorption of deuterium-irradiated graphite to demonstrate the in situ capabilities of this new facility.

Instruments & Instrumentation↗

DOE OSTI2021

Post-irradiation examination of legacy high burnup fuel to support safety testing

Safety/transient testing to evaluate performance under off-normal conditions is an essential pillar for both the development of Accident Tolerant Fuels (ATF) and the optimization of fuel operation economics beyond current discharge burnups. Among other factors, the successful interpretation of the transient testing results relies upon the knowledge of the initial conditions of the test, including the characteristics of the fuel system under scrutiny. When testing pre-irradiated material, the assumptions that the fuel and the cladding still have the same properties as in the pre-irradiation stage is obviously wrong and could affect the results of the test. This is particularly true the more burnup accumulates in the fuel rod and irradiation progresses. The knowledge of the initial microstructure of both fuel and cladding allows a clearer interpretation of the subsequent transient testing results, provides validation of the physical phenomena underlying the model predictions and eliminates the uncertainties related to the limited knowledge of the sample status before the test. One example is the phenomenon of fine fragmentation that occurs in Light Water reactor (LWR) fuel. During a Loss of Coolant Accident (LOCA) or Reactivity Initiated Transient (RIA) the fuel can severely fragment. During LOCA, high burnup fuel tend to finely fragment, which has raised safety concerns due to the increased likelihood of dispersal of such small particles once the cladding has burst and due to the increased fission gas release. Therefore, efforts have been devoted to the assessment of a pulverization threshold that could determine the conditions under which fine fragmentation is predominant. However, the lack of information regarding the initial conditions of the fuel, and the connections between those conditions and the pre-transient irradiation history, have hindered the development of a fully mechanistic fragmentation and pulverization criterion. The empirical relationships rely on conservative estimations, due to the lack of information on critical material properties and characteristics. More generally, experimental evidence of the irradiation-induced modifications at microstructural scale are necessary to determine the behavior of the material at the macroscopic scale, with the latter being the one of technological interest. Significant progress has been made in the last two decades in the developments of analytical materials science techniques that can be applied to highly radioactive materials, such as high burnup fuels. The availability of new techniques and the improvement of existing ones has enabled investigations previously not possible that can deepen the understanding of the fuel characteristics and properties at high burnup. The better knowledge of material behavior and irradiation-induced phenomena could help the prediction of its performance. In this context, the scope of the present work is to apply a wide portfolio of advanced characterization techniques to determine properties that are relevant for safety and performance. The results are interpreted in the context of engineering scale post-irradiation examinations and available information on the irradiation conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

FIB-ToF-SIMS characterization of irradiated U-10Zr

Post-irradiation examination (PIE) is critical for the performance assessment and qualification of nuclear fuels. Secondary ion mass spectrometry (SIMS) is a powerful materials characterization technique that allows for elemental and isotopic mapping with a depth resolution greater than EDS and EPMA. However, it has not yet been applied to PIE of metallic nuclear fuel. Here, in this work, we characterize an fast neutron spectrum irradiated U-10Zr fuel sample using a time-of-flight SIMS (ToF-SIMS) system connected to a FIB/SEM system, which allows for flexible sample analysis compared to a dedicated ToF-SIMS instrument. Analysis of the resulting hyperspectral micrograph data was aided by the development of an unsupervised machine learning (ML) algorithm that iterates on existing methods to segment the 3D micrographic datasets based on the similarity of mass spectra. The results showed that the FIB-ToF-SIMS instrument was potentially capable of spatially resolving closed fission gas bubbles in 3D by continued ion sputtering of the analyzed volume. Additionally, the ML algorithm proved useful in revealing the chemical segregation of light fission products (those with an atomic mass between approximately 85–105 amu, such as ruthenium and rhodium) plus matrix zirconium, heavy fission products (those with an atomic mass between approximately 135–150 amu, such as the lanthanides) and uranium. Future studies are planned to conduct FIB-ToF-SIMS analysis on more irradiated U-Zr samples to study the constituent redistribution.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Orbitally selective resonant photodoping to enhance superconductivity

Signatures of superconductivity at elevated temperatures above T c in high-temperature superconductors have been observed near 1/8 hole doping for photoexcitation with infrared or optical light polarized either in the CuO 2 plane or along the c axis. While the use of in-plane polarization has been effective for incident energies aligned to specific phonons, c-axis laser excitation in a broad range between 5 μm and 400 nm was found to affect the superconducting dynamics in striped La 1.88 5Ba 0.115 CuO 4 , with a maximum enhancement in the 1/ω dependence to the conductivity observed at 800 nm. This broad energy range, specifically 800 nm, is not resonant with any phonon modes, yet induced electronic excitations appear to be connected to superconductivity at energy scales well above the typical gap energies in the cuprates. A critical question is, What can be responsible for such an effect at 800 nm? Using time-dependent exact diagonalization, we demonstrate that the holes in the CuO 2 plane can be photoexcited into the charge reservoir layers at resonant wavelengths within a multiband Hubbard model. This orbitally selective photoinduced charge transfer effectively changes the in-plane doping level, which can lead to an enhancement of T c near the 1/8 anomaly.

36 MATERIALS SCIENCE↗

DOE OSTI2024

The Future of Vehicle Grid Integration: Harnessing the Flexibility of EV Charging

This document lays out a shared vision for a beneficial, EV-integrated future where EVs are safely and securely connected, reliably served, and harmonized with the electric grid. It was developed as part of the U.S. Department of Energy’s (DOE) EVGrid Assist initiative. Stakeholder input was gathered through individual and collective conversations, including eight listening sessions with more than 100 participants representing utilities of different sizes and operating structures, manufacturers of vehicles and chargers, national associations, standards organizations, Tribes, fleet managers, consumer advocates, charging network operators, community-based organizations, utility regulators, consultants, vendors, labor, and environmental justice organizations. This document focuses on the future of electric on-road U.S. transportation, specifically the integration of light-duty vehicles (LDV) and medium- and heavy-duty vehicles (MHDV) and their charging infrastructure with the electric grid. However, many of the insights here may apply to electrifying other transportation modes, as well as other distributed energy resources (DER).

EVGrid Assist initiative, EV-integrated future, el↗

DOE OSTI2024

The Future of Vehicle Grid Integration: Harnessing the Flexibility of EV Charging

EVGrid Assist initiative, EV-integrated future, el↗

DOE OSTI2023

Electromagnetic signatures of a chiral quantum spin liquid

Quantum spin liquids (QSL) have emerged as a captivating subject within interacting spin systems that exhibit no magnetic ordering even at the lowest temperature accessible experimentally. However, definitive experimental evidence remains elusive. In light of the recent surge in theoretical and experimental interest in the half-filled Hubbard model on a triangular lattice, which offers the potential for stabilizing a chiral QSL, we investigate the electromagnetic signatures of this phase to facilitate experimental detection. Utilizing a combination of parton mean-field theory and unbiased density-matrix renormalization group calculations, we systematically examine the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL. Additionally, we calculate the longitudinal and transverse optical conductivities below the Mott gap. Furthermore, employing quantum field theory analysis, we unravel the connection between spinon excitations and emergent as well as physical gauge fields. Our results demonstrate that the chiral QSL phase exhibits a distinct electromagnetic response, even within a Mott insulator regime. This finding holds great potential for enabling the experimental detection of this long-sought-after phase.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Understanding Heterogeneities in Quantum Materials

Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. Finally, the understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Non-perturbative quarkonium dissociation rates in strongly coupled quark-gluon plasma

Heavy quarks and quarkonia are versatile probes of the transport properties of the hot QCD medium produced in ultra-relativistic heavy-ion collisions (URHICs). A robust description of heavy-flavor transport coefficients requires a microscopic approach that treats the open and hidden heavy-flavor sectors on the same footing. Here, we employ the quantum many-body T -matrix formalism to evaluate the dissociation rates of heavy quarkonia in the quark-gluon plasma (QGP). The basic ingredient is the heavy-light T -matrix, which utilizes a nonperturbative driving kernel constrained by lattice-QCD data. Its resummation in a ladder series provides a much enhanced interaction strength compared to a previously used perturbative coupling to the quasiparticle partons in the QGP. The in-medium quarkonium properties, particularly their temperature-dependent binding energies, are obtained from selfconsistent calculations with the same interaction kernel, including interference effects (also referred to as the imaginary part of the heavy-quark potential) as well as off-shell parton spectral functions. We systematically investigate the interplay of these effects and elaborate on the connections to the dipole approximation used in effective field theory.

effective field theories of QCD↗

DOE OSTI2020

Comparative study on the overall energy performance between photovoltaic and Low-E insulated glass units

In this report a novel semi-transparent building integrated photovoltaic (BIPV) laminate was developed and introduced in this paper. It was produced by cutting standard mono-crystalline silicon solar cells into small strips and then making electrical connections between each strip before laminating the cells between two layers of glass. The overall energy performance and energy saving potential of the BIPV insulated glass unit (IGU) under real world conditions were identified through a side by side comparative study. Compared to the reference IGU, the BIPV IGU had lower solar heat gain coefficient (SHGC) but much higher U-factor. The average HVAC electricity saving of the BIPV IGU was about 10% relative to the reference IGU. Daylighting measurement and analysis were carried out to evaluate the trade-offs associated with the BIPV IGU between daylight, glare, and lighting energy use. The results indicated that the BIPV IGU is better than the reference IGU in reducing discomfort glare. However, if the most conservative viewpoint near the window is used for the assessment, a lower transmittance BIPV IGU is required to bring the overall discomfort levels below the perceptible level. Lastly, the net energy saving potential associated with the novel BIPV IGU was identified based on the power, thermal and daylighting performance. On average, the BIPV IGU saved 16.8% of the total electricity use of the room. Further studies and improvement on the energy conversion efficiency of solar cells, the optimal transmittance as well as the thermal properties would make this technology more energy-efficient and affordable.

14 SOLAR ENERGY↗

DOE OSTI2020

Status of weak scale supersymmetry after LHC Run 2 and ton-scale noble liquid WIMP searches

After completion of LHC Run 2, the ATLAS and CMS experiments had collected of order 139 fb –1 of data at √s = 13 TeV. While discovering a very Standard Model-like Higgs boson of mass m h ≃ 125 GeV, no solid signal for physics beyond the Standard Model has emerged so far at LHC. In addition, no WIMP signals have emerged so far at ton-scale noble liquid WIMP search experiments. For the case of weak scale supersymmetry (SUSY), which is touted as a simple and elegant solution to the gauge hierarchy problem and likely low energy limit of compactified string theory, LHC has found rather generally that gluinos are beyond about 2.2 TeV whilst top squark must lie beyond 1.1 TeV. These limits contradict older simplistic notions of naturalness that emerged in the 1980s–1990s, leading to the rather pessimistic view that SUSY is now excluded except for perhaps some remaining narrow corners of parameter space. Yet, this picture ignores several important developments in SUSY/string theory that emerged in the 21st century: 1. the emergence of the string theory landscape and its solution to the cosmological constant problem, 2. a more nuanced view of naturalness including the notion of “stringy naturalness”, 3. the emergence of anomaly-free discrete R-symmetries and their connection to R-parity, Peccei-Quinn symmetry, the SUSY μ problem and proton decay and 4. the importance of including a solution to the strong CP problem. Rather general considerations from the string theory landscape favor large values of soft terms, subject to the vacuum selection criteria that electroweak symmetry is properly broken (no charge and/or color breaking (CCB) minima) and the resulting magnitude of the weak scale is not too far from our measured value. Then stringy naturalness predicts a Higgs mass m h ~ 125 GeV whilst sparticle masses are typically lifted beyond present LHC bounds. Lastly, in light of these refinements in theory perspective confronted by LHC and dark matter search results, we review the most likely LHC, ILC and dark matter signatures that are expected to arise from weak scale SUSY as we understand it today.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Nonlinear encoding in diffractive information processing using linear optical materials

Nonlinear encoding of optical information can be achieved using various forms of data representation. Here, we analyze the performances of different nonlinear information encoding strategies that can be employed in diffractive optical processors based on linear materials and shed light on their utility and performance gaps compared to the state-of-the-art digital deep neural networks. For a comprehensive evaluation, we used different datasets to compare the statistical inference performance of simpler-to-implement nonlinear encoding strategies that involve, e.g., phase encoding, against data repetition-based nonlinear encoding strategies. We show that data repetition within a diffractive volume (e.g., through an optical cavity or cascaded introduction of the input data) causes the loss of the universal linear transformation capability of a diffractive optical processor. Therefore, data repetition-based diffractive blocks cannot provide optical analogs to fully connected or convolutional layers commonly employed in digital neural networks. However, they can still be effectively trained for specific inference tasks and achieve enhanced accuracy, benefiting from the nonlinear encoding of the input information. Our results also reveal that phase encoding of input information without data repetition provides a simpler nonlinear encoding strategy with comparable statistical inference accuracy to data repetition-based diffractive processors. Our analyses and conclusions would be of broad interest to explore the push-pull relationship between linear material-based diffractive optical systems and nonlinear encoding strategies in visual information processors.

42 ENGINEERING↗

DOE OSTI2026

Tensor-polarized parton density in the 𝑁 → Δ transition from the large-𝑁 𝑐 light-cone wave function

The tensor-polarized parton density is defined by the forward matrix element of a partonic operator in the 𝑁 → Δ transition. In this work, we investigate it by employing the large-𝑁 𝑐 light-cone wave function derived from the mean-field approach. The mean-field picture is based on low-energy effective dynamics in the large-𝑁 𝑐 limit, where the baryon wave function is formulated in the rest frame. By exploiting the covariance of the mean-field solution, we derive the corresponding large-𝑁 𝑐 light-cone wave function—decomposed unambiguously into 3⁢𝑄 , 5⁢𝑄 , 7⁢𝑄 , and higher Fock components—in the infinite momentum frame. Evaluating the overlap of these wave functions, we derive an overlap representation of the tensor-polarized parton density in the 𝑁 → Δ transition and find that the leading contribution arises from the 5⁢𝑄 Fock sector. This indicates that the tensor-polarized parton density directly probes the genuine 5⁢𝑄 component and is governed by chiral dynamics. Our numerical analysis shows that the 𝑁 → Δ tensor-polarized parton density is suppressed, consistent with standard large-𝑁 𝑐 expectations. Finally, we establish connections among the tensor-polarized parton density, the generalized parton distribution 𝐻 𝑋 , and the energy-momentum tensor form factor 𝐹 4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Zero curvature is a necessary and sufficient condition for a spin-orbital decomposition

There has been an extended debate regarding the existence of a spin-orbital decomposition of the angular momentum of photons and other massless particles. It was recently shown that there are both geometric and topological obstructions preventing any such decomposition. Here we show that any geometric connection on a particle’s state space induces a splitting of the angular momentum into two operators. These operators are well-defined angular momentum operators if and only if the connection has zero curvature. Massive particles have two canonical curved connections corresponding to boosts and rotations, respectively. Furthermore, these can be uniquely combined to produce a flat connection, and this gives a novel derivation of the Newton-Wigner position operator and the corresponding spin and orbital angular momenta for relativistic massive particles. When the mass is taken to zero, transverse boosts and rotations degenerate, leaving only a single connection for massless particles. This connection produces a commonly proposed splitting of the massless angular momentum into two operators. However, the connection is not flat, explaining why these operators do not satisfy the angular momentum commutation relations and are thus not true spin and orbital angular momentum operators.

Angular momentum↗