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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Energy-momentum tensor in Φ 4 theory at one loop

The energy-momentum tensor form factors are studied in Φ 4 theory to one-loop order with particular focus on the 𝐷-term, a particle property which has attracted a lot of attention in the recent literature. It is shown that the free Klein-Gordon theory value of the 𝐷-term 𝐷 free =−1 is reduced to 𝐷 one-loop =− $\frac{1}{3}$ even if the Φ 4 interaction is infinitesimally small. A companion work in Φ 3 theory confirms this result which may indicate that it is independent of the type of interaction as long as the scalar theory is renormalizable. Dispersion relations are studied. Various definitions of mean square radii including the mechanical radius are investigated. The findings contribute to a better understanding of the energy momentum tensor properties of particles and their interpretation.

form factors↗
NASA NTRS1975

Gravitational theories with nonzero divergence of the energy-momentum tensor

Assuming that the divergence of the energy-momentum tensor is nonzero leads to a class of theories with consistent field equations and gauge conditions as well as compatibility with the Newtonian limit of the conservation laws. Both the Einstein and the Brans-Dicke theories are used as models, but the extension to other viable theories such as vector-metric and two-metric theories is possible. One particularly interesting theory emerges that agrees with the ordinary Brans-Dicke theory except for the post-Newtonian parameter zeta sub 2, which predicts nonconservation of total momentum. Unfortunately, no accurate experimental limits for this parameter are known. It thus remains for future experiments in lunar-laser ranging to test this theory.

Smalley, L. L.↗
DOE OSTI2025

Geometric origin of the energy-momentum tensor improvement terms

In a flat background, the canonical energy momentum tensor of Lorentz and conformally invariant matter field theories can be improved to a symmetric and traceless tensor that gives the same conserved charges. We argue that the geometric origin of this improvement process is unveiled when the matter theory is coupled to metric-affine gravity. In particular, we show that the Belinfante-Rosenfeld improvement terms correspond to the matter theory’s hypermomentum. The improvement terms in conformally invariant matter theories are also related to the hypermomentum; however, a general proof would require an extended investigation. We demonstrate our results through various examples, such as the free massless scalar, the Maxwell field, Abelian p-forms, the Dirac field, and a nonunitary massless scalar field. Possible applications of our method for theories that break Lorentz or special conformal invariance are briefly discussed.

classical solutions in field theory↗
DOE OSTI2026

Reflections on Noether’s second theorem and the energy-momentum tensor

Through symmetry of the action under global spacetime translations, Noether’s first theorem infamously entails an energy-momentum tensor (EMT) that is neither symmetric nor gauge-invariant. In a prior work [Phys. Rev. D 106, 125012 (2022)], I had obtained a symmetric and gauge-invariant EMT by using Noether’s second theorem instead, with local spacetime translations as the symmetry group. However, the derivation therein was flawed, containing a faulty assumption about the transformation rule for spinor fields. In this work, I revisit the derivation of the previous work, both correcting the faulty step and simplifying the derivation for broader accessibility. The end result is an EMT for quantum chromodynamics that is gauge-invariant, but not symmetric.

Quantum chromodynamics↗
DOE OSTI2025

Energy-momentum tensor in the 2D Ising CFT in full modular space

A set of lattice operators for the energy-momentum (EM) tensor in the Ising CFT is derived in the spin variables. Our expression works under arbitrary affine transformation both on triangular and hexagonal lattices (where the former includes the rectangular lattices). The correctness of the operators is numerically confirmed in Monte Carlo calculations by comparing the results with the conformal Ward identity, including the operator normalization. In the derivation of the EM tensor, a staggered structure of the affine-transformed hexagonal lattice is analyzed, which shows a peculiar shift from the circumcenter dual lattice and appears as a mixing angle between the holomorphic part $T(z)$ and the antiholomorphic part $\tilde T(\bar z)$. The details of this contribution will appear in a subsequent paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1974

Modified Brans-Dicke gravitational theory with nonzero divergence of the energy-momentum tensor

The Brans-Dicke theory of gravitation is modified by assuming that the divergence of the energy-momentum tensor is proportional to the covariant derivative of the scalar curvature. No ad hoc additions to the usual Brans-Dicke field equations are required as in Rastall's modification of the Einstein theory or as in the steady-state theories, of which this is a natural possibility. Three parameters emerge from the theory - namely, the unnormalized gravitational constant, the usual Brans-Dicke parameter, and the proportionality constant. In the post-Newtonian approximation, these parameters can be fixed by experiment. However, there exists a certain choice of the parameters for which the theory reduces to an Einstein theory with constant scalar curvature.

Smalley, L. L.↗
DOE OSTI2026

Energy-momentum tensor in a classical model of the electron

We show that the leading nonanalytic terms in the small-𝑡 expansion of the energy-momentum tensor form factors of an electrically charged particle in QED can be correctly derived in a classical model of the electron by Białynicki-Birula. Based on the lucidity of the employed exactly solvable model, we comment also on the recently proposed concept of a regularized proton 𝐷-term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Inevitable inflation in Einstein-Cartan theory with improved energy-momentum tensor with spin

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.

Fennelly, A. J.↗
NASA NTRS1988

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

Fennelly, A. J.↗
DOE OSTI2026

The Kinetic-Energy–Momentum–Mass 5-Flux of a Baryon Fluid in Bargmann Spacetimes

A Bargmann spacetime is a constrained five-dimensional setting that, while introducing no new physical degrees of freedom beyond those of ordinary four-dimensional spacetime, permits Galilei physics to be expressed with a tensor formalism that respects the distinction between mass and energy while affording the conceptual and technical advantages of a spacetime metric. This framework offers a route to a strong-field ‘Galilei general relativity’ approximating the usual Poincaré general relativity introduced by Einstein. In preparation for modeling core-collapse supernovae, where such an approximation would be useful, this work generalizes the kinetic-energy–momentum–mass 5-flux 𝒯 and its associated spacetime tensor law from a simple fluid of constant particle mass to a baryon fluid whose multiple nuclear species can interconvert rest mass and internal energy. The spacetime tensor law on Bargmann–Galilei spacetime 𝐵𝒢 and its decompositions relative to comoving (‘Lagrangian’) and fiducial (‘Eulerian’) observers are derived in detail. The formalism is rendered more suitable for core-collapse supernova modeling by an extension from strict 𝐵𝒢 to a regime that might be denoted as 𝐵𝒢+: microscopically Poincaré yet macroscopically Galilei. This extension accommodates energy generation by nuclear composition changes and allows comoving energy density and pressure to contribute relative to mass density, while preserving the simplifications of Galilei bulk fluid flow and the streamlined geometry governed by the Bargmann–Galilei spacetime metric.

Cardall, Christian [ORNL] (ORCID:000000020086105X)↗
DOE OSTI2025

Energy-momentum-conserving stochastic differential equations and algorithms for the nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

Improved perfect-fluid energy-momentum tensor with spin in Einstein-Cartan space-time

The description of the spin given here is classical in that it is intrinsic but not quantized. The approach in this matter is similar to, for example, the work of Bailey and Israel (1973, 1975, 1979), where the fluid particles, which have intrinsic spin, may be galaxies or clusters of galaxies. The elementary particles of these objects and the 'ferromagnetic alignment' of their quantum spins are not resorted to in order to describe a fluid with spin. Physically this means that the equation of motion for the spin tensor is a modified Fermi-Walker transport equation (Misner et al., 1973), arising as a direct result of the inclusion of spin as an intrinsic variable in the thermodynamic description of the internal energy. The variables in this description are classical variables throughout and are not microscopic fields. An improved perfect-fluid energy-momentum tensor that includes spin and torsion is presented. Use is made of a Lagrangian variational principle based on the tetrad formalism of Halbwach (1960) and the method od constraints of Ray (1972).

Ray, J. R.↗
DOE OSTI2024

Initial energy-momentum to final flow: A general framework for heavy-ion collisions

The evolution of a relativistic heavy-ion collision is typically understood as a process that transmutes the initial geometry of the system into the final momentum distribution of observed hadrons, which can be described via a cumulant expansion of the initial distribution of energy density and is represented at leading order as the well-known eccentricity scaling of anisotropic flow. We extend this framework to include the contribution from initial momentum-space properties, as encoded in other components of the energy-momentum tensor. Furthermore, we confirm the validity of the framework in state-of-the-art hydrodynamic simulations of large and small systems. With this framework, it is possible to separate the effects of early time dynamics from those of final-state evolution, even in the case when the distribution of energy does not fully determine subsequent evolution, as for example, in small systems. Specifically, we answer the question of when and how azimuthal correlations from the initial state survive to the final state. In very small systems such as 𝑝−𝑝, for example, initial momentum degrees of freedom dominate over energy. Thus, even if the system forms a quark-gluon plasma that is well described by hydrodynamics, the usual hydrodynamic picture of the transmutation of initial geometry to final momentum anisotropy is broken. Nevertheless, we show that the hydrodynamic response to the full energy-momentum tensor can be well understood in a similar manner as larger systems. Additionally, this framework elucidates the generic features of the system's evolution that are responsible for the impressive success of hydrodynamic simulations, but which may still hold even in cases where hydrodynamics is not applicable.

Relativistic heavy-ion collisions↗
NASA NTRS1992

Solar-wind/magnetospheric dynamos: MHD-scale collective entry of the solar wind energy, momentum and mass into the magnetosphere

A quasi open MHD (Magnetohydrodynamic) scale anomalous transport controlled boundary layer model is proposed, where the MHD collective behavior of magnetofluids (direct dynamo effect, anomalous viscous interaction and anomalous diffusion of the mass and the magnetic field) plays the main role in the conversion of the Solar Wind (SW) kinetic and magnetic energy into electromagnetic energy in the Magnetosphere (MSp). The so called direct and indirect dynamo effects are based on inductive and purely dissipative energy conversion, respectively. The self organization ability of vector fields in turbulent magnetofluids implies an inductive response of the plasma, which leads to the direct dynamo effect. The direct dynamo effect describes the direct formation of localized field aligned currents and the transverse Alfven waves and provides a source for MHD scale anomalous diffusivity and viscosity. The SW/MSp coupling depends on the dynamo efficiency.

Song, Yan↗
NASA NTRS1974

Do massive Brans-Dicke theories of gravitation imitate Brans-Dicke theories with nonzero divergence of energy-momentum tensor

Acharya and Hogan (1973) have introduced a massive scalar field into the usual Brans-Dicke (1961) theory of gravitation. Formally they obtain certain field equations. The assumption of a nonzero divergence for T mu nu (or equivalently the introduction of sources) formally imitates a massive Brans-Dicke and satisfies the condition of Acharya and Hogan that the theory be indistinguishable with the classical test of the Einstein theory. Although it was shown elsewhere that the modified Brans-Dicke theory agrees with the classical test under certain conditions, there were no specified limits on omega, a similar circumstance discovered by Acharya and Hogan for the massive scalar field.

Smalley, L. L.↗