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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 OSTI2016

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. In conclusion, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Gravitomagnetism and Spinor Quantum Mechanics

We give a systematic treatment of a spin 1=2 particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it is largely self-contained and may serve as an introduction to spinors in a Riemann space. The analysis is based on the Dirac equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The restriction to a slowly moving matter source, such as the earth, allows us to describe the gravitational field by a gravitoelectric (Newtonian) potential and a gravitomagnetic (frame-dragging) vector potential, the existence of which has recently been experimentally verified. Our main interest is the coupling of the orbital and spin angular momenta of the particle to the gravitomagnetic field. Specifically we calculate the gravitational gyromagnetic ratio as g{sub g} = 1 ; this is to be compared with the electromagnetic gyromagnetic ratio of g{sub e} = 2 for a Dirac electron.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Flat minimal quantizations of Stäckel systems and quantum separability

In this paper, we consider the problem of quantization of classical Stäckel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of Stäckel transform, natural Hamiltonian systems from a given Riemann space are expressed by some flat coordinates of related Euclidean configuration space. Then, the so-called flat minimal quantization procedure is applied in order to construct an appropriate Hermitian operator in the respective Hilbert space. Finally, we distinguish a class of Stäckel systems which remains separable after any of admissible flat minimal quantizations. - Highlights: • Using Stäckel transform, separable Hamiltonians are expressed by flat coordinates. • The concept of admissible flat minimal quantizations is developed. • The class of Stäckel systems, separable after minimal flat quantization is established. • Separability of related stationary Schrödinger equations is presented in explicit form.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

An inverse theorem on 'economic' maps

We prove that the bound from the theorem on 'economic' maps is best possible. Namely, for m>n+d we construct a map from an n-dimensional simplex to an m-dimensional Euclidean space for which (and for any close map) there exists a d-dimensional plane whose preimage has cardinality not less than the upper bound [(dn+n+1)/(m-n-d)]+d from the theorem on 'economic' maps. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Field-theoretical formulation of Regge–Teitelboim gravity

Theory of gravity is considered in the Regge–Teitelboim approach in which the pseudo-Rimannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of a field theory in which the original pseudo-Rimannian space is defined by the field constant-value surfaces. The symmetry properties of the proposed theory are investigated, and possible structure of the field-theoretical Lagrangian is discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Geometry of the electron local observables

We show that the complete set of the second power identities for the electron local observables consists of 36 equations. The identities connect the products of the electron bilinear forms and, being considered as geometrically meaningful equations in 3D Euclidean space, are separated over the groups of equations for the scalar, vector and tensor quantities. Considering the complete set of identities as a set of the second power equations, we solve the equations and find the irreducible representation for the electron local observables. The representation defines the 16 electron local observables as functions of 7 basic parameters and can be formulated in 6 various forms. The basic parameters include scalar and pseudoscalar, the time components of a 4-vector and a 4-pseudovector, and three Euler angles which define the angular position of a local 3D frame with respect to the 3D laboratory frame. These 7 parameters completely define the space components of the 4-vector and the 4-pseudovector, as well as the polar and axial vectors. The developed representation shows that the analysis of the any electron wave packet can be considerably simplified by the reduction of the number of analyzed real functions from 16 to 7. As an example, we present the structure of the local observables defined by the irreducible representation in a case of a traveling electron wave. - Highlights: > Complete set of bilinear identities for the electron observables is derived. > Irreducible representation for the electron observables is found. > The representation defines the electron observables as functions of 7 parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

The theory of shell-based Q-mappings in geometric function theory

Open, discrete Q-mappings in R{sup n}, n{>=}2, Q element of L{sup 1}{sub loc}, are proved to be absolutely continuous on lines, to belong to the Sobolev class W{sub loc}{sup 1,1}, to be differentiable almost everywhere and to have the N{sup -1}-property (converse to the Luzin N-property). It is shown that a family of open, discrete shell-based Q-mappings leaving out a subset of positive capacity is normal, provided that either Q has finite mean oscillation at each point or Q has only logarithmic singularities of order at most n-1. Under the same assumptions on Q it is proved that an isolated singularity x{sub 0} element of D of an open discrete shell-based Q-map f:D/{l_brace}x{sub 0{r_brace}{yields}}R-bar{sup n} is removable; moreover, the extended map is open and discrete. On the basis of these results analogues of the well-known Liouville, Sokhotskii-Weierstrass and Picard theorems are obtained. Bibliography: 34 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Integral estimates for differentiable functions on irregular domains

Integral representations for functions and their partial derivatives in terms of some fixed system of partial derivatives are constructed on irregular domains in a Euclidean space. Embedding theorems for Sobolev-type spaces into a Lebesgue space are established and the norms of the derivatives are estimated. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Neighbourly polytopes with few vertices

A family of neighbourly polytopes in R{sup 2d} with N=2d+4 vertices is constructed. All polytopes in the family have a planar Gale diagram of a special type, namely, with exactly d+3 black points in convex position. These Gale diagrams are parametrized by 3-trees (trees with a certain additional structure). For all polytopes in the family, the number of faces of dimension m containing a given vertex A depends only on d and m. Bibliography: 7 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

On the measure of conformal difference between Euclidean and Lobachevsky spaces

Euclidean space R{sup n} and Lobachevsky space H{sup n} are known to be not equivalent either conformally or quasiconformally. In this work we give exact asymptotics of the critical order of growth at infinity for the quasiconformality coefficient of a diffeomorphism f:R{sup n}{yields}H{sup n} for which such a mapping f is possible. We also consider the general case of immersions f:M{sup n}{yields}N{sup n} of conformally parabolic Riemannian manifolds. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Boundary conditions and consistency of effective theories

Effective theories are nonlocal at the scale of the eliminated heavy particles modes. The gradient expansion, which represents such nonlocality, must be truncated to have treatable models. This step leads to the proliferation of the degrees of freedom, which renders the identification of the states of the effective theory nontrivial. Furthermore, it generates nondefinite metric in the Fock space, which in turn endangers the unitarity of the effective theory. It is shown that imposing a generalized Kubo-Martin-Schwinger boundary conditions for the new degrees of freedom leads to reflection positivity for a wide class of Euclidean effective theories, thereby these lead to acceptable theories when extended to real-time.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Computation of the spectral density of two-point functions: Complex masses, cut rules, and beyond

We present a steepest descent calculation of the Kaellen-Lehmann spectral density of two-point functions involving complex conjugate masses in Euclidean space. This problem occurs in studies of (gauge) theories with Gribov-like propagators. As the presence of complex masses and the use of Euclidean space brings the theory outside of the strict validity of the Cutkosky cut rules, we discuss an alternative method based on the Widder inversion operator of the Stieltjes transformation. It turns out that the results coincide with those obtained by naively applying the cut rules. We also point out the potential usefulness of the Stieltjes (inversion) formalism when nonstandard propagators are used, in which case cut rules are not available at all.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Optical metrics and projective equivalence

Trajectories of light rays in a static spacetime are described by unparametrized geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the Universe as static may determine the geometry of the light rays differently. More specifically, we classify Lorentzian metrics admitting more than one hyper-surface orthogonal timelike Killing vector and analyze the projective equivalence of the resulting optical metrics. These metrics are shown to be projectively equivalent up to diffeomorphism if the static Killing vectors generate a group SL(2,R), but not projectively equivalent in general. We also consider the cosmological C metrics in Einstein-Maxwell theory and demonstrate that optical metrics corresponding to different values of the cosmological constant are projectively equivalent.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Renormalizability of the linearly broken formulation of the BRST symmetry in the presence of the Gribov horizon in Landau gauge Euclidean Yang-Mills theories

In previous work by M. A. L. Capri, A. J. Gomez, M. S. Guimaraes, V. E. R. Lemes, S. P. Sorella, and D. G. Tedesco [Phys. Rev. D 82, 105019 (2010)], we have shown that the soft breaking of the Becchi-Rouet-Stora-Tyutin (BRST) symmetry arising within the Gribov-Zwanziger framework can be converted into a linear breaking, while preserving the nilpotency of the BRST operator. Because of its compatibility with the quantum action principle, the linearly broken BRST symmetry directly translates into a set of Slavnov-Taylor identities. We show that these identities guarantee the multiplicative renormalizability of both Gribov-Zwanziger and refined Gribov-Zwanziger theories to all orders. The known property that only two renormalization factors are needed is recovered. The nonrenormalization theorem of the gluon-ghost-antighost vertex, as well as the renormalization factor of the Gribov parameter, are derived within the linearly broken formulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Glueball Masses from an Infrared Moment Problem

We set up an infrared-based moment problem to obtain estimates of the masses of the scalar, pseudoscalar, and tensor glueballs in Euclidean Yang-Mills theories using the refined Gribov-Zwanziger (RGZ) version of the Landau gauge, which takes into account nonperturbative physics related to gauge copies. Employing lattice input for the mass scales of the RGZ gluon propagator, the lowest order moment problem approximation gives the values m{sub 0++}{approx_equal}1.96 GeV, m{sub 2++}{approx_equal}2.04 GeV, and m{sub 0-+}{approx_equal}2.19 GeV in the SU(3) case, all within a 20% range of the corresponding lattice values. We also recover the mass hierarchy m{sub 0++}<m{sub 2++}<m{sub 0-+}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Boundary Value Problems for Nonclassical Systems of Second Order Differential Equations

We study boundary value problems for systems of second order differential equations with principal part in the form of the squared first order differential operator. We establish the unique solvability of the boundary value problem for a nonclassical system in the plane, which can be regarded as the Riemann–Hilbert problem with discontinuous boundary conditions. Similar problems are considered in the space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Virasoro minimal string

We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge c ≥ ≥ 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter c c and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of JT gravity. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.

Physics↗