Symmetry and Covariance of Non-relativistic Quantum Mechanics
Omote, Minoru; kamefuchi, Susumu
2000-01-01
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.
Covariant geometric quantization of non-relativistic Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time.
Generalized Linear Covariance Analysis
Carpenter, James R.; Markley, F. Landis
2014-01-01
This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.
General covariance in computational electrodynamics
DEFF Research Database (Denmark)
Shyroki, Dzmitry; Lægsgaard, Jesper; Bang, Ole;
2007-01-01
We advocate the generally covariant formulation of Maxwell equations as underpinning some recent advances in computational electrodynamics—in the dimensionality reduction for separable structures; in mesh truncation for finite-difference computations; and in adaptive coordinate mapping as opposed...
Multivariate covariance generalized linear models
DEFF Research Database (Denmark)
Bonat, W. H.; Jørgensen, Bent
2016-01-01
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...... are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions...
General Covariance in Gravity at a Lifshitz Point
Horava, Petr
2011-01-01
This paper is based on the invited talks delivered by the author at GR 19: the 19th International Conference on General Relativity and Gravitation, Ciudad de M\\'exico, M\\'exico, July 2010. In Part 1, we briefly review some of the main features of quantum gravity with anisotropic scaling, and comment on its possible relation to the causal dynamical triangulations (CDT) approach to lattice quantum gravity. Part 2 explains the construction of gravity with anisotropic scaling with an extended gauge symmetry -- essentially a nonrelativistic version of general covariance. This extra symmetry eliminates the scalar graviton polarization, and thus brings the theory closer to general relativity at long distances.
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
GenASiS: General Astrophysical Simulation System. II. Nonrelativistic Hydrodynamics
Cardall, Christian Y; Endeve, Eirik; Mezzacappa, Anthony
2012-01-01
In this paper, the second in a series, we document the algorithms and solvers for compressible nonrelativistic hydrodynamics implemented in GenASiS (General Astrophysical Simulation System)---a new code being developed initially and primarily, though by no means exclusively, for the simulation of core-collapse supernovae. In the Mathematics division of GenASiS we introduce Solvers, which includes finite-volume updates for generic hyperbolic BalanceEquations and ordinary differential equation integration Steps. We also introduce the Physics division of GenASiS; this extends the Manifolds division of Mathematics into physical Spaces, defines StressEnergies, and combines these into Universes. We benchmark the hydrodynamics capabilities of GenASiS against many standard test problems; the results illustrate the basic competence of our implementation, demonstrate the manifest superiority of the HLLC over the HLL Riemann solver in a number of interesting cases, and provide preliminary indications of the code's abili...
General Covariance from the Quantum Renormalization Group
Shyam, Vasudev
2016-01-01
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Po...
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Beneke, M.; Hellmann, C.; Ruiz-Femenia, P.
2012-01-01
We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are prerequisites to the calculation of the Sommerfeld enhancement in the MSSM, which will be presented in subsequent work. They can also be used to obtain concise analytic expressions for MSSM dark matter pair annihilation in the present Universe for a large number of exc...
A Generalized Autocovariance Least-Squares Method for Covariance Estimation
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad;
2007-01-01
A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter.......A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter....
General relativistic Boltzmann equation, I: Covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
Generalized linear models with coarsened covariates: a practical Bayesian approach.
Johnson, Timothy R; Wiest, Michelle M
2014-06-01
Coarsened covariates are a common and sometimes unavoidable phenomenon encountered in statistical modeling. Covariates are coarsened when their values or categories have been grouped. This may be done to protect privacy or to simplify data collection or analysis when researchers are not aware of their drawbacks. Analyses with coarsened covariates based on ad hoc methods can compromise the validity of inferences. One valid method for accounting for a coarsened covariate is to use a marginal likelihood derived by summing or integrating over the unknown realizations of the covariate. However, algorithms for estimation based on this approach can be tedious to program and can be computationally expensive. These are significant obstacles to their use in practice. To overcome these limitations, we show that when expressed as a Bayesian probability model, a generalized linear model with a coarsened covariate can be posed as a tractable missing data problem where the missing data are due to censoring. We also show that this model is amenable to widely available general-purpose software for simulation-based inference for Bayesian probability models, providing researchers a very practical approach for dealing with coarsened covariates.
Lorentz Transformation and General Covariance Principle
Kleyn, Aleks
2008-01-01
I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn few physical applications: dynamics and Lorentz transformation in gravitational fields, Doppler shift. A reference frame in event space is a smooth field of orthonormal bases. Every reference frame is equipped by anholonomic coordinates. Using anholonomic coordinates allows to find out relative speed of two observers and appropriate Lorentz transformation. Synchronization of a reference frame is an anholonomic time coordinate. Simple calculations show how synchronization influences time measurement in the vicinity of the Earth. Measurement of Doppler shift from the star orbiting the black hole helps to determine mass of the black hole. We call a manifold with torsion and nonmetricity the metric\\hyph affine manifold. The nonmetricity leads to a difference between the auto para...
Khoury, Justin; Tolley, Andrew J
2014-01-01
Traditional derivations of general relativity from the graviton degrees of freedom assume space-time Lorentz covariance as an axiom. In this essay, we survey recent evidence that general relativity is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not a property of space-time. This result has revolutionary implications for fundamental physics.
Hui, Yi; Law, Siu Seong; Ku, Chiu Jen
2017-02-01
Covariance of the auto/cross-covariance matrix based method is studied for the damage identification of a structure with illustrations on its advantages and limitations. The original method is extended for structures under direct white noise excitations. The auto/cross-covariance function of the measured acceleration and its corresponding derivatives are formulated analytically, and the method is modified in two new strategies to enable successful identification with much fewer sensors. Numerical examples are adopted to illustrate the improved method, and the effects of sampling frequency and sampling duration are discussed. Results show that the covariance of covariance calculated from responses of higher order modes of a structure play an important role to the accurate identification of local damage in a structure.
Time and Fermions: General Covariance vs. Ockham's Razor for Spinors
Pitts, J Brian
2015-01-01
It is a commonplace attributed to Kretschmann that any local physical theory can be represented in arbitrary coordinates using tensor calculus. But the literature also claims that spinors _as such_ cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent, so what is general covariance for fermions? In fact both commonplaces are wrong. Ogievetsky and Polubarinov (OP) constructed spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn nonlinear group representations. Roughly and locally, OP spinors resemble the orthonormal basis or tetrad formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The tetrad formalism is thus de-Ockhamized, with six extra components and six compensating gauge symmetries. As developed nonperturbatively by Bilyalov, OP spinors admit any coordinates at a point, but 'time' must be listed first; 'time' is defined by an eigenvalue problem involving the metric and diag(-1,1,1,1), t...
Dynamical Relativistic Systems and the Generalized Gauge Fields of Manifestly Covariant Theories
Horwitz, L P
1998-01-01
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii et al showed that the resulting evolution contains a stochastic flow in phase space to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistically charged particle in interaction with the electromagnetic field. We review the standard derivation of the covariant Lorentz force, and review the structure of the relativistic equations used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field. We show how this agreement is achieved, and criticize some of the fundamental assumptions underlying these derivations. We argue that a more complete theory, involving ``off-shell'' electromagnetic fields should be utilized. We then discuss the formulation of the off-shell electromagne...
Nonrelativistic Geodesic Motion
Mangiarotti, L
1999-01-01
We show that any second order dynamic equation on a configuration space $X\\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics.
Covariant Magnetic Connection Hypersurfaces
Pegoraro, F
2016-01-01
In the single fluid, nonrelativistic, ideal-Magnetohydrodynamic (MHD) plasma description magnetic field lines play a fundamental role by defining dynamically preserved "magnetic connections" between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D {\\it magnetic connection hypersurfaces} in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when ${\\bf E} \\cdot {\\bf B} = 0$.
Some remarks on the notions of general covariance and background independence
Giulini, Domenico
2006-01-01
In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange argument that Einstein put forward in his 1913 "Entwurf paper" with M. Grossmann to discredit scalar theories of gravity in order to promote general covariance.
Osp(1,2)-covariant Lagrangian quantization of general gauge theories
Energy Technology Data Exchange (ETDEWEB)
Geyer, B.; Lavrov, P.M. [Universitat Leipzig, Naturwissenschaftlich-Theoretisches Zentrum, Leipzig (Germany); Muelsch, D. [Wissenschaftszentrum Leipzig e.V., Leipzig (Germany)
1998-10-01
An osp(1, 2)-covariant Lagrangian quantization of general gauge theories is introduced which also applies to massive fields. It generalizes the Batalin-Vilkovisky and the Sp(2)-covariant field-antifield approach and guarantees symplectic invariance of the quantized action. Massive gauge theories with closed algebra are considered as an example. (author)
A cautionary note on generalized linear models for covariance of unbalanced longitudinal data
Huang, Jianhua Z.
2012-03-01
Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome this and other challenges by embedding the covariance matrix of the observed data for each subject in a larger covariance matrix and employing the familiar EM algorithm to compute the maximum likelihood estimates of the parameters and their standard errors. We illustrate and assess the methodology using real data sets and simulations. © 2011 Elsevier B.V.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-15
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
FBST for covariance structures of generalized Gompertz models
Maranhão, Viviane Teles de Lucca; Lauretto, Marcelo De Souza; Stern, Julio Michael
2012-10-01
The Gompertz distribution is commonly used in biology for modeling fatigue and mortality. This paper studies a class of models proposed by Adham and Walker, featuring a Gompertz type distribution where the dependence structure is modeled by a lognormal distribution, and develops a new multivariate formulation that facilitates several numerical and computational aspects. This paper also implements the FBST, the Full Bayesian Significance Test for pertinent sharp (precise) hypotheses on the lognormal covariance structure. The FBST's e-value, ev(H), gives the epistemic value of hypothesis, H, or the value of evidence in the observed in support of H.
One-parameter nonrelativistic supersymmetry for microtubules
Rosu, H C
2003-01-01
The simple supersymmetric model of Caticha [PRA 51, 4264 (1995)], as used by Rosu [PRE 55, 2038 (1997)] for microtubules, is generalized to the case of Mielnik's one-parameter nonrelativistic susy [JMP 25, 3387 (1984)
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue; GUO Jin-yun
2005-01-01
The unknown parameter's variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now,which didn't appear in the internal and external referencing documents. The unknown parameter's variance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source,multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann equati
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann
Lompay, Robert R
2013-01-01
Arbitrary diffeomorphically invariant metric-torsion theories of gravity are considered. It is assumed that Lagrangians of such theories contain derivatives of field variables (tensor densities of arbitrary ranks and weights) up to a second order only. The generalized Klein-Noether methods for constructing manifestly covariant identities and conserved quantities are developed. Manifestly covariant expressions are constructed without including auxiliary structures like a background metric. In the Riemann-Cartan space, the following \\emph{manifestly generally covariant results} are presented: (a) The complete generalized system of differential identities (the Klein-Noether identities) is obtained. (b) The generalized currents of three types depending on an arbitrary vector field displacements are constructed: they are the canonical Noether current, symmetrized Belinfante current and identically conserved Hilbert-Bergmann current. In particular, it is stated that the symmetrized Belinfante current does not depen...
Pion generalized parton distributions within a fully covariant constituent quark model
Energy Technology Data Exchange (ETDEWEB)
Fanelli, Cristiano [Massachusetts Institute of Technology, Cambridge, MA (United States). Lab. for Nuclear Science; Pace, Emanuele [' ' Tor Vergata' ' Univ., Rome (Italy). Physics Dept.; INFN Sezione di TorVergata, Rome (Italy); Romanelli, Giovanni [Rutherford-Appleton Laboratory, Didcot (United Kingdom). STFC; Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Salmistraro, Marco [Rome La Sapienza Univ. (Italy). Physics Dept.; I.I.S. G. De Sanctis, Rome (Italy)
2016-05-15
We extend the investigation of the generalized parton distribution for a charged pion within a fully covariant constituent quark model, in two respects: (1) calculating the tensor distribution and (2) adding the treatment of the evolution, needed for achieving a meaningful comparison with both the experimental parton distribution and the lattice evaluation of the so-called generalized form factors. Distinct features of our phenomenological covariant quark model are: (1) a 4D Ansatz for the pion Bethe-Salpeter amplitude, to be used in the Mandelstam formula for matrix elements of the relevant current operators, and (2) only two parameters, namely a quark mass assumed to be m{sub q} = 220 MeV and a free parameter fixed through the value of the pion decay constant. The possibility of increasing the dynamical content of our covariant constituent quark model is briefly discussed in the context of the Nakanishi integral representation of the Bethe-Salpeter amplitude. (orig.)
Knecht, Stefan; Jensen, Hans Jorgen Aa; Fleig, Timo
2008-01-07
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.
BAYESIAN LOCAL INFLUENCE ASSESSMENTS IN A GROWTH CURVE MODEL WITH GENERAL COVARIANCE STRUCTURE
Institute of Scientific and Technical Information of China (English)
2000-01-01
The objective of this paper is to present a Bayesian approach based on Kullback Leibler divergence for assessing local influence in a growth curve model with general covariance structure.Under certain prior distribution assumption,the Kullback-Leibler divergence is used to measure the influence of some minor perturbation on the posterior distribution of unknown parameter.This leads to the diagnostic statistic for detecting which response is locally influential.As an application,the common covariance-weighted perturbation scheme is thoroughly considered.
Conformal generally covariant quantum field theory. The scalar field and its Wick products
Energy Technology Data Exchange (ETDEWEB)
Pinamonti, N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2008-06-15
In this paper we generalize the construction of generally covariant quantum theories given in [R. Brunetti, K. Fredenhagen, R. Verch, Commun. Math. Phys. 237, 31 (2003)] to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale {mu} appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields. (orig.)
Di Girolami, Cristina
2011-01-01
This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\\'etivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We investigate some $C^{1}$ type transformations for various classes of stochastic processes admitting a $\\chi$-quadratic variation and related properties. If $\\X^1$ and $\\X^2$ admit a $\\chi$-covariation, $F^i: B_i \\rightarrow \\R$, $i = 1, 2$ are of class $C^1$ with some supplementary assumptions then the covariation of the real processes $F^1(\\X^1)$ and $F^2(\\X^2)$ exist. A detailed analysis will be devoted to the so-called window processes. Let $X$ be a real continuous process; the $C([-\\tau,0])$-valued process $X(\\cdot)$ defined by $X_t(y)...
Covariant second-order perturbations in generalized two-field inflation
Tzavara, Eleftheria; van Tent, Bartjan
2014-01-01
We examine the covariant properties of generalized models of two-field inflation, with non-canonical kinetic terms and a non-trivial field metric. We demonstrate that kinetic-term derivatives and covariant field derivatives do commute in a proper covariant framework, which was not realized before in the literature. We also define a set of generalized slow-roll parameters, using a unified notation. Within this framework, we study the most general case of models that allows for well-defined sound speeds, which we identify as the models with parallel momentum and field velocity vectors. For these models we write the exact cubic action in terms of the adiabatic and isocurvature perturbations. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale for these generalized models. We illustrate our general results by considering their long-wavelength limit, as well as with the example of two-field DBI inflation.
Covariant second-order perturbations in generalized two-field inflation
Energy Technology Data Exchange (ETDEWEB)
Tzavara, Eleftheria; Tent, Bartjan van [Laboratoire de Physique Théorique, Université Paris-Sud 11 and CNRS, Bâtiment 210, 91405 Orsay Cedex (France); Mizuno, Shuntaro, E-mail: Eleftheria.Tzavara@th.u-psud.fr, E-mail: Shuntaro.Mizuno@apc.univ-paris7.fr, E-mail: Bartjan.Van-Tent@th.u-psud.fr [Laboratoire Astroparticule et Cosmologie (APC), UMR 7164-CNRS, Université Denis Diderot-Paris 7, 10 rue Alice Domon et Léonie Duquet, 75205 Paris (France)
2014-07-01
We examine the covariant properties of generalized models of two-field inflation, with non-canonical kinetic terms and a possibly non-trivial field metric. We demonstrate that kinetic-term derivatives and covariant field derivatives do commute in a proper covariant framework, which was not realized before in the literature. We also define a set of generalized slow-roll parameters, using a unified notation. Within this framework, we study the most general class of models that allows for well-defined adiabatic and entropic sound speeds, which we identify as the models with parallel momentum and field velocity vectors. For these models we write the exact cubic action in terms of the adiabatic and isocurvature perturbations. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale for these generalized models. We illustrate our general results by considering their long-wavelength limit, as well as with the example of two-field DBI inflation.
Surprises with Nonrelativistic Naturalness
Horava, Petr
2016-01-01
We explore the landscape of technical naturalness for nonrelativistic systems, finding surprises which challenge and enrich our relativistic intuition already in the simplest case of a single scalar field. While the immediate applications are expected in condensed matter and perhaps in cosmology, the study is motivated by the leading puzzles of fundamental physics involving gravity: The cosmological constant problem and the Higgs mass hierarchy problem.
Scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity
Nishimura, J; Tsuchiya, A; Jun Nishimura; Shinya Tamura; Asato Tsuchiya
1994-01-01
Using (2+$\\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$ minimal conformal matter. In the spectrum appear all the scaling dimensions of the scaling operators in the matrix model except the boundary operators, while there are also many others which have no corresponding scaling dimensions in the matrix model.
Unification of SU(2)xU(1) Using a Generalized Covariant Derivative and U(3)
Chaves, M
1998-01-01
A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify and unify the Glashow-Weinberg-Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.
Quantization of Maxwell's equations on curved backgrounds and general local covariance
Dappiaggi, Claudio
2011-01-01
We develop a quantization scheme for Maxwell's equations without source on an arbitrary four dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends from a vector potential. It is shown that, in general, the associated field algebra can contain a non trivial centre and, on account of this, such a theory cannot be described within the framework of general local covariance unless further restrictive assumptions on the topology of the spacetime are made.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Generally Covariant Maxwell Theory for Media with a Local Response: Progress since 2000
Hehl, Friedrich W; Obukhov, Yuri N
2016-01-01
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure of electrodynamics (conservation of electric charge and magnetic flux). Moreover, it is ideally suited for applying it to media with local (and mainly linear) response behavior. We try to collect the new knowledge that grew out of this development. We would like to ask the participants of EMTS 2016 to inform us of work that we may have overlooked in our review.
Exotic Non-relativistic String
Casalbuoni, Roberto; Longhi, Giorgio
2007-01-01
We construct a classical non-relativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the non-commutative structure of the model. Under double dimensional reduction the model reduces to the exotic non-relativistic particle in 2+1 dimensions.
More On Nonrelativistic Diffeomorphism Invariance
Andreev, Oleg
2014-01-01
Certain aspects of nonrelativistic diffeomorphisms in 2+1 dimensions are investigated. These include a nonrelativistic limit of some relativistic actions in 3 dimensions, the Seiberg-Witten map, a modification of the viscosity tensor in particular due to a non-uniform magnetic field, a redefinition of background fields, and 1/R terms on Riemann surfaces of constant curvature.
Non-relativistic particles in a thermal bath
Directory of Open Access Journals (Sweden)
Vairo Antonio
2014-04-01
Full Text Available Heavy particles are a window to new physics and new phenomena. Since the late eighties they are treated by means of effective field theories that fully exploit the symmetries and power counting typical of non-relativistic systems. More recently these effective field theories have been extended to describe non-relativistic particles propagating in a medium. After introducing some general features common to any non-relativistic effective field theory, we discuss two specific examples: heavy Majorana neutrinos colliding in a hot plasma of Standard Model particles in the early universe and quarkonia produced in heavy-ion collisions dissociating in a quark-gluon plasma.
DEFF Research Database (Denmark)
Holst, René; Jørgensen, Bent
2015-01-01
The paper proposes a versatile class of multiplicative generalized linear longitudinal mixed models (GLLMM) with additive dispersion components, based on explicit modelling of the covariance structure. The class incorporates a longitudinal structure into the random effects models and retains...... a marginal as well as a conditional interpretation. The estimation procedure is based on a computationally efficient quasi-score method for the regression parameters combined with a REML-like bias-corrected Pearson estimating function for the dispersion and correlation parameters. This avoids...... the multidimensional integral of the conventional GLMM likelihood and allows an extension of the robust empirical sandwich estimator for use with both association and regression parameters. The method is applied to a set of otholit data, used for age determination of fish....
Model Checking for a General Linear Model with Nonignorable Missing Covariates
Institute of Scientific and Technical Information of China (English)
Zhi-hua SUN; Wai-Cheung IP; Heung WONG
2012-01-01
In this paper,we investigate the model checking problem for a general linear model with nonignorable missing covariates.We show that,without any parametric model assumption for the response probability,the least squares method yields consistent estimators for the linear model even if only the complete data are applied.This makes it feasible to propose two testing procedures for the corresponding model checking problem:a score type lack-of-fit test and a test based on the empirical process.The asymptotic properties of the test statistics are investigated.Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-(r),0 ≤ (r) ＜ 1/2.Simulation results show that both tests perform satisfactorily.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona
Titov, V. S.
2007-01-01
The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coordinates. At least two overlapping regular systems of coordinates for each of the boundaries are necessary in this case to avoid spherical-pole-like singularities in the coordinates of the footpoints. This implies that the basic characteristic of magnetic connectivity-the squashing degree or factor Q of elemental flux tubes, according to Titov and coworkers-must be rewritten in covariant form. Such a covariant expression of Q is derived in this work. The derived expression is very flexible and highly efficient for describing the global magnetic connectivity in the solar corona. In addition, a general expression for a new characteristic Q1, which defines a squashing of the flux tubes in the directions perpendicular to the field lines, is determined. This new quantity makes it possible to filter out the quasi-separatrix layers whose large values of Q are caused by a projection effect at the field lines nearly touching the photosphere. Thus, the value Q1 provides a much more precise description of the volumetric properties of the magnetic field structure. The difference between Q and Q1 is illustrated by comparing their distributions for two configurations, one of which is the Titov-Demoulin model of a twisted magnetic field.
Inflation in general covariant Ho\\v{r}ava-Lifshitz gravity without projectability
Zhu, Tao; Wang, Anzhong
2012-01-01
In this paper, we study inflation in the general covariant Ho\\v{r}ava-Lifshitz gravity without the projectability condition. We write down explicitly the equations of the linear scalar perturbations of the FRW universe for a single scalar field without specifying to any gauge. Applying these equations to a particular gauge, we are able to obtain a master equation of the perturbations, in contrast to all the other versions of the theory without the projectability condition. This is because in the current version of the theory it has the same degree of freedom of general relativity. To calculate the power spectrum and index, we first define the initial conditions as the ones that minimize the energy of the ground state. Then, we obtain the full solutions of the equation of motion, by using the WKB approximations. From these solutions, we calculate the power spectrum and spectrum index of the comoving curvature perturbations and find the corrections due to the high order spatial derivative terms of the theory to...
Gravitational radiation of angular—momentum from general covariant conservation law
Institute of Scientific and Technical Information of China (English)
冯世祥; 宗红石
1996-01-01
The quadrupole angular-momentum radiation of gravity is obtained from the recently obtained covariant conservation law of angular-momentum.The result agrees with that derived from the Landau-Lifshitz energy-momentum pseudo-tensor.
Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
Griffin, Tom; Horava, Petr; Yan, Ziqi
2015-01-01
Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion $\\omega\\sim k^n$ ($n=2,3,\\ldots$), whose naturalness is protected by polynomial shift symmetries. Here we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of $n$ changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.
Fields and fluids on curved non-relativistic spacetimes
Geracie, Michael; Roberts, Matthew M
2015-01-01
We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example of this approach we develop the theory of non-relativistic dissipative fluids and find significant differences in both equations of motion and allowed transport coefficients from those found previously. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its rela...
Fredi, André; Nolis, Pau; Cobas, Carlos; Martin, Gary E.; Parella, Teodor
2016-05-01
The current Pros and Cons of a processing protocol to generate pure chemical shift NMR spectra using Generalized Indirect Covariance are presented and discussed. The transformation of any standard 2D homonuclear and heteronuclear spectrum to its pure shift counterpart by using a reference DIAG spectrum is described. Reconstructed pure shift NMR spectra of NOESY, HSQC, HSQC-TOCSY and HSQMBC experiments are reported for the target molecule strychnine.
Fredi, André; Nolis, Pau; Cobas, Carlos; Martin, Gary E; Parella, Teodor
2016-05-01
The current Pros and Cons of a processing protocol to generate pure chemical shift NMR spectra using Generalized Indirect Covariance are presented and discussed. The transformation of any standard 2D homonuclear and heteronuclear spectrum to its pure shift counterpart by using a reference DIAG spectrum is described. Reconstructed pure shift NMR spectra of NOESY, HSQC, HSQC-TOCSY and HSQMBC experiments are reported for the target molecule strychnine.
Al-Hashimi, M H; Shalaby, A M
2016-01-01
A general method has been developed to solve the Schr\\"odinger equation for an arbitrary derivative of the $\\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A distinction in the treatment has been made between the case when the derivative $n$ is an even number from the one when $n$ is an odd number. A general gap equations for each case has been derived. The case of $\\delta^{(2)}$-function potential has been used as an example. The results from the relativistic case show that the $\\delta^{(2)}$-function system behaves exactly like the $\\delta$-function and the $\\delta'$-function potentials, which means it also shares the same features with quantum field theories, like being asymptotically free, in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. As a result the evidence of universality of contact interactions has been extended further to include the $\\delta^{(2)}$-functi...
Newton-Cartan (super)gravity as a non-relativistic limit
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativit
Edmondson, J K
2014-01-01
Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and the generating vector field, and is provided for from two equivalent perspectives: a Lagrangian specification with respect to a generalized parameter, and an Eulerian specification making explicit the evolution dynamics. Furthermore, we provide explicit non-trivial conditions which govern the transformation properties of the referential gradient object.
Nonrelativistic Fermions in Magnetic Fields a Quantum Field Theory Approach
Espinosa, Olivier R; Lepe, S; Méndez, F
2001-01-01
The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible regularizations. The nonrelativistic grand-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2+1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function.
Graviton Loop Corrections to Vacuum Polarization in de Sitter in a General Covariant Gauge
Glavan, D; Prokopec, Tomislav; Woodard, R P
2015-01-01
We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations.
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary coordinat
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary
Non-relativistic classical mechanics for spinning particles
Salesi, G
2004-01-01
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.
Gravity duals for nonrelativistic conformal field theories.
Balasubramanian, Koushik; McGreevy, John
2008-08-08
We attempt to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.
Non-Relativistic Spacetimes with Cosmological Constant
Aldrovandi, R.; Barbosa, A. L.; Crispino, L.C.B.; Pereira, J. G.
1998-01-01
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible ...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
The renormalization of composite operators in Yang-Mills theories using general covariant gauge
Collins, J C; John C Collins; Randall J Scalise
1994-01-01
Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have "alien" gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infra-red singularities that appear when gluonic matrix elements are taken on-shell at zero momentum transfer. % Keywords: twist-two covariant gluon operator, mixing, non-abelian, anomalous dimension, Ward identity, BRST, LSZ reduction, Dixon, Taylor, Joglekar, Lee.
Land, M C
2001-01-01
This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schr\\"odinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the non-relativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is lnear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformat...
Vortex dynamics in nonrelativistic Abelian Higgs model
Directory of Open Access Journals (Sweden)
A.A. Kozhevnikov
2015-11-01
Full Text Available The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background. The equations for the time derivatives of the curvature and the torsion of the vortex contour generalizing the Betchov–Da Rios equations in hydrodynamics, are obtained. They are applied to study the conservation of helicity of the gauge field forming the vortex, twist, and writhe numbers of the vortex contour. It is shown that the conservation of helicity is broken when both terms in the equation of the vortex motion are present, the first due to the exchange of excitations of the phase and modulus of the scalar field and the second one due to the coupling of the gauge field forming the vortex, with the fermion asymmetric background.
Microscopic picture of non-relativistic classicalons
Energy Technology Data Exchange (ETDEWEB)
Berkhahn, Felix; Müller, Sophia; Niedermann, Florian; Schneider, Robert, E-mail: felix.berkhahn@physik.lmu.de, E-mail: sophia.x.mueller@physik.uni-muenchen.de, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 Munich (Germany)
2013-08-01
A theory of a non-relativistic, complex scalar field with derivatively coupled interaction terms is investigated. This toy model is considered as a prototype of a classicalizing theory and in particular of general relativity, for which the black hole constitutes a prominent example of a classicalon. Accordingly, the theory allows for a non-trivial solution of the stationary Gross-Pitaevskii equation corresponding to a black hole in the case of GR. Quantum fluctuations on this classical background are investigated within the Bogoliubov approximation. It turns out that the perturbative approach is invalidated by a high occupation of the Bogoliubov modes. Recently, it was proposed that a black hole is a Bose-Einstein condensate of gravitons that dynamically ensures to stay at the verge of a quantum phase transition. Our result is understood as an indication for that claim. Furthermore, it motivates a non-linear numerical analysis of the model.
Lamb Shift in Nonrelativistic Quantum Electrodynamics.
Grotch, Howard
1981-01-01
The bound electron self-energy or Lamb shift is calculated in nonrelativistic quantum electrodynamics. Retardation is retained and also an interaction previously dropped in other nonrelativistic approaches is kept. Results are finite without introducing a cutoff and lead to a Lamb shift in hydrogen of 1030.9 MHz. (Author/JN)
Primordial Non-Gaussianity of Gravitational Waves in General Covariant Ho\\v{r}ava-Lifshitz Gravity
Huang, Yongqing; Yousefi, Razieh; Zhu, Tao
2013-01-01
In this paper, we study 3-point correlation function of primordial gravitational waves generated in the de Sitter background in the framework of the general covariant Ho\\v{r}ava-Lifshitz gravity with an arbitrary coupling constant $\\lambda$. We find that, to the leading order, the interaction Hamiltonian receives contributions from four terms built of the 3-dimensional Ricci tensor $R_{ij}$ of the leaves $t = $ constant. In particular, the 3D Ricci scalar $R$ yields the same $k$-dependence as that in general relativity, but with different magnitude due to coupling with the U(1) field $A$ and a UV history. The two terms $R_{ij} R^{ij}$ and $(\
Soo, Chopin
2014-01-01
Covariance of space and time in General Relativity (GR) entails a number of technical and conceptual difficulties. These can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. A theory of gravity with this paradigm shift, from quantum to classical regimes, is presented; GR is contained as a special case. Appositely formulated as a master constraint, the Hamiltonian constraint now determines only dynamics; and is relieved of its dual role of generating symmetry transformations, and the consequent baggage of multi-fingered evolution with arbitrary lapse functions is absent. The Dirac algebra, with 4-dimensional diffeomorphism symmetry on-shell, is replaced by the master constraint algebra which possesses only spatial diffeomorphism gauge symmetry, both on- and off-shell. Decomposition of the spatial metric into unimodular and determinant, q, factors results in clean separation of the canonical variables. The classical...
Salisbury, Donald; Sundermeyer, Kurt
2015-01-01
Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic spacetime curvature based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semi-classical quantizations. The scheme calls into question Wheeler's geometrodynamical approach and the associated Wheeler-DeWitt equation in which three-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light...
Holographic thermalization from nonrelativistic branes
Roychowdhury, Dibakar
2016-05-01
In this paper, based on the fundamental principles of gauge/gravity duality and considering a global quench, we probe the physics of thermalization for certain special classes of strongly coupled nonrelativistic quantum field theories that are dual to an asymptotically Schrödinger D p brane space time. In our analysis, we note that during the prelocal stages of the thermal equilibrium the entanglement entropy has a faster growth in time compared to its relativistic cousin. However, it shows a linear growth during the postlocal stages of thermal equilibrium where the so-called tsunami velocity associated with the linear growth of the entanglement entropy saturates to that of its value corresponding to the relativistic scenario. Finally, we explore the saturation region and it turns out that one must constraint certain parameters of the theory in a specific way in order to have discontinuous transitions at the point of saturation.
Paynter, S.; Nachabe, M.
2008-12-01
One of the most important tools in water management is the accurate forecast of both long-term and short- term extreme values for both flood and drought conditions. Traditional methods of trend detection, such as ordinary least squares (OLS) or the Mann-Kendall test, are not aptly suited for hydrologic systems while traditional methods of predicting extreme flood and drought frequencies, such as distribution fitting without parameter covariates, may be highly inaccurate in lake-type systems, especially in the short-term. In the case of lakes, traditional frequency return estimates assume extremes are independent of trend or starting lake stages. However, due to the significant autocorrelation of lake levels, the initial stage can have a significant influence on the severity of a given event. The aim of this research was to accurately identify the direction and magnitude of trends in flood and drought stages and provide more accurate predictions of both long-term and short-term flood and drought stage return frequencies utilizing the generalized extreme value distribution with time and starting stage covariates. All of the lakes researched evidenced either no trend or very small trends unlikely to significantly alter prediction of future flood or drought return levels. However, for all of the lakes significant improvement in the prediction of extremes was obtained with the inclusion of starting lake stage as a covariate. Traditional methods of predicting flood or drought stages significantly overpredict stages when starting lake stages are low and underpredict stages when starting stages are high. The difference between these predictions can be nearly two meters, a significant amount in urbanized watersheds in areas of the world with flat topography. Differences of near two meters can mean significant alterations in evacuation or other water management decisions. In addition to improving prediction of extreme events, utilizing GEV with time or starting stage
Entropy Production and Equilibrium Conditions of General-Covariant Spin Systems
Directory of Open Access Journals (Sweden)
Wolfgang Muschik
2015-12-01
Full Text Available In generalizing the special-relativistic one-component version of Eckart’s continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry as presented by Schouten (Schouten, J.A. Ricci-Calculus, 1954 and Blagojevic (Blagojevic, M. Gauge Theories of Gravitation, 2013 we consider the entropy production and other thermodynamical quantities, such as the entropy flux and the Gibbs fundamental equation. We discuss equilibrium conditions in gravitational theories, which are based on such geometries. In particular, thermodynamic implications of the non-symmetry of the energy-momentum tensor and the related spin balance equations are investigated, also for the special case of general relativity.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
Energy Technology Data Exchange (ETDEWEB)
Ko, Sung Moon [Department of Physics, Sogang University,Seoul 121-742 (Korea, Republic of); Melby-Thompson, Charles M. [Kavli Institute for the Physics and Mathematics of the Universe (WPI),The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo,Kashiwanoha, Kashiwa, 277-8583 (Japan); Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI),The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo,Kashiwanoha, Kashiwa, 277-8583 (Japan); Park, Jeong-Hyuck [Department of Physics, Sogang University,Seoul 121-742 (Korea, Republic of)
2015-12-22
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (‘non-geometry’), but even locally (‘non-Riemannian’). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri http://dx.doi.org/10.1063/1.1372697 arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of http://dx.doi.org/10.1016/j.nuclphysb.2014.01.003 on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
Directory of Open Access Journals (Sweden)
Rodolfo Casana
2016-01-01
Full Text Available We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions, ω1(|ϕ| and ω(|ϕ|, which split the kinetic term of the Higgs field, |Dμϕ|2→ω1(|ϕ||D0ϕ|2-ω(|ϕ||Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whether ω(|ϕ|∝β|ϕ|2β-2 with β≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing function ω1(|ϕ| which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual |ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.
Meng, Jin-Liu; Zhou, Xian-Hui; Zhao, Zhi-Gang; Du, Guo-Zhen
2008-09-01
Theory predicts that tighter correlation between floral traits and weaker relationship between floral and vegetative traits more likely occur in specialized flowers than generalized flowers, favoring by precise fit with pollinators. However, traits and trait correlations frequently vary under different environments. Through detecting spatiotemporal variation in phenotypic traits (floral organ size and vegetative size) and trait correlations in four Ranunculaceae species, we examined four predictions. Overall, our results supported these predictions to a certain degree. The mean coefficient of variation (CV) of floral traits in two specialized species (Delphinium kamaonense and Aconitum gymnandrum) was marginally significantly lower than that of another two generalized species (Trollius ranunculoides and Anemone obtusiloba). The two specialized species also showed marginally significantly smaller CV in floral traits than vegetative size across the two species. The absolute mean correlation between floral and vegetative traits, or that between floral traits in species with specialized flowers was not significantly lower, or higher than that in generalized plants, weakly supporting the predictions. Furthermore, we documented a large variation in trait correlations of four species among different seasons and populations. Study of covariance of floral and vegetative traits will benefit from the contrast of results obtained from generalized and specialized pollination systems.
Institute of Scientific and Technical Information of China (English)
Jin-Liu Meng; Xian-Hui Zhou; Zhi-Gang Zhao; Guo-Zhen Du
2008-01-01
Theory predicts that tighter correlation between floral traits and weaker relationship between floral and vegetative traits more likely occur in specialized flowers than generalized flowers,favoring by precise fit with pollinators.However,traits and trait correlations frequently vary under different environments.Through detecting spatiotemporal variation in phenotypic traits (floral organ size and vegetative size) and trait correlations in four Ranunculaceae species,we examined four predictions.Overall,our results supported these predictions to a certain degree.The mean coefficient of variation (CV) of floral traits in two specialized species (Delphinium kamaonense and Aconitum gymnandrum) was marginally significantly lower than that of another two generalized species (Trollius ranunculoides and Anemone obtusiloba).The two specialized species also showed marginally significantly smaller CV in floral traits than vegetative size across the two species.The absolute mean correlation between floral and vegetative traits,or that between floral traits in species with specialized flowers was not significantly lower,or higher than that in generalized plants,weakly supporting the predictions.Furthermore,we documented a large variation in trait correlations of four species among different seasons and populations.Study of covariance of floral and vegetative traits will benefit from the contrast of results obtained from generalized and specialized pollination systems.
Do non-relativistic neutrinos oscillate?
Akhmedov, Evgeny
2017-07-01
We study the question of whether oscillations between non-relativistic neutrinos or between relativistic and non-relativistic neutrinos are possible. The issues of neutrino production and propagation coherence and their impact on the above question are discussed in detail. It is demonstrated that no neutrino oscillations can occur when neutrinos that are non-relativistic in the laboratory frame are involved, except in a strongly mass-degenerate case. We also discuss how this analysis depends on the choice of the Lorentz frame. Our results are for the most part in agreement with Hinchliffe's rule.
Effective action of composite fields for general gauge theories in BLT-covariant formalism
Lavrov, P M; Reshetnyak, A A
1996-01-01
The gauge dependence of the effective action of composite fields for general gauge theories in the framework of the quantization method by Batalin, Lavrov and Tyutin is studied. The corresponding Ward identites are obtained. The variation of composite fields effective action is found in terms of new set of generators depending on composite field. The theorem of the on-shell gauge fixing independence for the effective action of composite fields in such formalism is proven. Brief discussion of gravitational-vector induced interaction for Maxwell theory with composite fields is given.
Energy Technology Data Exchange (ETDEWEB)
Lavrov, P.M.; Odintsov, S.D. [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634041 (Russia)]|[Department ECM, Faculte de Fisica, Universidad de Barcelona, Diagonal 647, 08028 Barcelona (Spain); Reshetnyak, A.A. [Quantum Field Theory Department, Tomsk State University, Tomsk 634050 (Russia)
1997-07-01
The gauge dependence of the effective action of composite fields for general gauge theories in the framework of the quantization method by Batalin, Lavrov and Tyutin is studied. The corresponding Ward identities are obtained. The variation of composite fields effective action is found in terms of new set of generators depending on composite field. The theorem of the on-shell gauge fixing independence for the effective action of composite fields in such formalism is proven. A brief discussion of gravitational-vector induced interaction for Maxwell theory with composite fields is given. {copyright} {ital 1997 American Institute of Physics.}
A projector formulation of the Galilean covariant Duffin-Kemmer-Petiau field
Energy Technology Data Exchange (ETDEWEB)
Santos, E S [Centro Federal de Educacao Tecnologica da Bahia, DCA-Coordenacao de Fisica, Rua Emidio Santos s/n, Barbalho, 40300-010 Salvador, BA (Brazil); Abreu, L M [Centro de Cincias Exatas e Tecnologicas, Universidade Federal do Reconcavo da Bahia, Campus de Cruz das Almas, 44380-000 Cruz das Almas, BA (Brazil)
2008-02-22
We construct in this paper a projector formulation of the Galilean covariant Duffin-Kemmer-Petiau field in five dimensions. Such an approach allows us to select the scalar and vector sectors of the theory through the use of the appropriate operators. As an application, we study a non-minimal coupling associated to the DKP harmonic oscillator, naturally in the non-relativistic regime and with the selection of the spin-0 sector in a general representation. We also discuss the local gauge invariance and the anomalous term which appear in the wave equations due to the minimal coupling. In both questions, our results were carried out as in the relativistic case, i.e. the consistent local gauge transformations can be obtained through the choice of the right form of the non-relativistic DKP field.
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
General covariance and the objectivity of space-time point-events
Lusanna, L
2005-01-01
"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The {\\it physical individuation} of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the {\\it Dirac observables}) that represent - as it were - the {\\it ontic} part of the metric field. The physical role of the {\\it epistemic} part (viz. the {\\it gauge} variables) is likewise clarified. At the end, a peculiar four-dimensional {\\it holistic and structuralist} view of space-time emerges which includes elements common to the tradition of both {\\it substantivalism} and {\\it relationism}. The observables of our models undergo real {\\it temporal change} and thereby provide a counter-example to the thesis of the {\\it frozen-time} picture of evolution. Invited Contribution to the ESF 2004 Oxford Conference on Space-Time
Entropy current for non-relativistic fluid
Banerjee, Nabamita; Jain, Akash; Roychowdhury, Dibakar
2014-01-01
We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the non-relativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermody...
Salisbury, Donald; Renn, Jürgen; Sundermeyer, Kurt
2016-02-01
Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic space-time curvature-based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semiclassical quantizations. The scheme calls into question Wheeler’s geometrodynamical approach and the associated Wheeler-DeWitt equation in which 3-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light of this new constrained Hamiltonian description. In particular, we show how the Kuchař multi-fingered time approach can be understood as a means of introducing full four-dimensional diffeomorphism invariants. Every choice of new phase space variables yields new Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic Schrödinger equations. We show how to implement this freedom by canonical transformation of the intrinsic Hamiltonian. We also reinterpret and rectify significant work by Dittrich on the construction of “Dirac observables.”
Nonrelativistic parallel shocks in unmagnetized and weakly magnetized plasmas
Niemiec, Jacek; Bret, Antoine; Wieland, Volkmar
2012-01-01
We present results of 2D3V particle-in-cell simulations of non-relativistic plasma collisions with absent or parallel large-scale magnetic field for parameters applicable to the conditions at young supernova remnants. We study the collision of plasma slabs of different density, leading to two different shocks and a contact discontinuity. Electron dynamics play an important role in the development of the system. While non-relativistic shocks in both unmagnetized and magnetized plasmas can be mediated by Weibel-type instabilities, the efficiency of shock-formation processes is higher when a large-scale magnetic field is present. The electron distributions downstream of the forward and reverse shocks are generally isotropic, whereas that is not always the case for the ions. We do not see any significant evidence of pre-acceleration, neither in the electron population nor in the ion distribution.
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
General coordinate invariance in quantum many-body systems
Brauner, Tomas; Monin, Alexander; Penco, Riccardo
2014-01-01
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the background metric and gauge fields, first introduced by Son and Wingate in 2005 and refined in subsequent works, follow naturally from our framework. Our approach makes it clear that Galilei or Poincare symmetry is by no means a necessary prerequisite for making the theory invariant under coordinate diffeomorphisms. General covariance merely expresses the freedom to choose spacetime coordinates at will, whereas the true, physical symmetries of the system can be separately implemented as "internal" symmetries within the vielbein formalism. A systematic way to implement such symmetries is provided by the coset construction. We illustrate this point by applying our formalism to nonrelativistic s-wave superfluids.
Soo, Chopin; Yu, Hoi-Lai
2013-12-01
Covariance of space and time in General Relativity (GR) entails a number of technical and conceptual difficulties. Remarkably, these can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. The framework for a theory of gravity with this paradigm shift, from quantum to classical regimes, is presented; GR is contained as a special case. Appositely formulated as a master constraint, the Hamiltonian constraint now determines only dynamics; and is relieved of its dual role of generating symmetry transformations. The Dirac algebra, in which 4-dimensional diffeomorphism symmetry is only realized on-shell, is replaced by the master constraint algebra which possesses only spatial diffeomorphism gauge symmetry, both on- and off-shell. Decomposition of the spatial metric into unimodular and determinant, q, factors results in mutually commuting pairs of canonical variables. The classical content of GR can be captured with a Hamiltonian constraint linear in the trace of the momentum. This implies a theory of quantum gravity can be described by a Schrodinger equation first order in intrinsic time ln q accompanied with positive semi-definite probability density. The semi-classical Hamilton-Jacobi equation is also first order in intrinsic time, with the implication of being complete; and gauge-invariant physical observables can be constructed from integration constants of its complete integral solution. Classical space-time, with direct correlation of its proper times and intrinsic time intervals, emerges from constructive interference; and the physical content of GR can be regained from a theory with a true Hamiltonian generating intrinsic time translations, but with only spatial diffeomorphism symmetry. The framework also prompts natural extensions towards a well-behaved quantum theory of gravity.
Noninertial effects on nonrelativistic topological quantum scattering
Mota, H. F.; Bakke, K.
2017-08-01
We investigate noninertial effects on the scattering problem of a nonrelativistic particle in the cosmic string spacetime. By considering the nonrelativistic limit of the Dirac equation we are able to show, in the regime of small rotational frequencies, that the phase shift has two contribution: one related to the noninertial reference frame, and the other, due to the cosmic string conical topology. We also show that both the incident wave and the scattering amplitude are altered as a consequence of the noninertial reference frame and depend on the rotational frequency.
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Kuckert, B; Kuckert, Bernd; Mund, Jens
2004-01-01
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Moruzzi, Sara; Ogliari, Anna; Ronald, Angelica; Happe, Francesca; Battaglia, Marco
2011-01-01
While social impairment, difficulties with communication, and restricted repetitive behaviors are central features of Autism Spectrum Disorders, physical clumsiness is a commonly co-occurring feature. In a sample of 398 twin pairs (aged 8-17 years) from the Italian Twin Registry we investigated the nature of the co-variation between a psychometric…
Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale
Lane, Charles D
2016-01-01
The notion of uniform and/or constant tensor fields of rank $>0$ is incompatible with general curved spacetimes. This work considers the consequences of certain tensor-valued coefficients for Lorentz violation in the Standard-Model Extension varying with spacetime position. We focus on two of the coefficients, $a_\\mu$ and $b_\\mu$, that characterize Lorentz violation in massive fermions, particularly in those fermions that constitute ordinary matter. We calculate the nonrelativistic hamiltonian describing these effects, and use it to extract the sensitivity of several precision experiments to coefficient variation.
Scattering theory the quantum theory of nonrelativistic collisions
Taylor, John R
2006-01-01
This graduate-level text is intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for readers who are already familiar with the general principles of quantum mechanics and who have some small acquaintance with scattering theory. Study of this text will allow students of atomic or nuclear physics to begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For students of high-energy physics, it provides the necessary background for later study of relativistic p
The covariance of GPS coordinates and frames
Energy Technology Data Exchange (ETDEWEB)
Lachieze-Rey, Marc [CNRS APC, UMR 7164 Service d' Astrophysique, CE Saclay, 91191 Gif sur Yvette Cedex (France)
2006-05-21
We explore, in the general relativistic context, the properties of the recently introduced global positioning system (GPS) coordinates, as well as those of the associated frames and coframes that they define. We show that they are covariant and completely independent of any observer. We show that standard spectroscopic and astrometric observations allow any observer to measure (i) the values of the GPS coordinates at his position (ii) the components of his 4-velocity and (iii) the components of the metric in the GPS frame. This provides this system with a unique value both for conceptual discussion (no frame dependence) and for practical use (involved quantities are directly measurable): localization, motion monitoring, astrometry, cosmography and tests of gravitation theories. We show explicitly, in the general relativistic context, how an observer may estimate his position and motion, and reconstruct the components of the metric. This arises from two main results: the extension of the velocity fields of the probes to the whole (curved) spacetime, and the identification of the components of the observer's velocity in the GPS frame with the (inversed) observed redshifts of the probes. Specific cases (non-relativistic velocities, Minkowski and Friedmann-Lemaitre spacetimes, geodesic motions) are studied in detail.
Nonrelativistic quantum X-ray physics
Hau-Riege, Stefan P
2015-01-01
Providing a solid theoretical background in photon-matter interaction, Nonrelativistic Quantum X-Ray Physics enables readers to understand experiments performed at XFEL-facilities and x-ray synchrotrons. As a result, after reading this book, scientists and students will be able to outline and perform calculations of some important x-ray-matter interaction processes. Key features of the contents are that the scope reaches beyond the dipole approximation when necessary and that it includes short-pulse interactions. To aid the reader in this transition, some relevant examples are discussed in detail, while non-relativistic quantum electrodynamics help readers to obtain an in-depth understanding of the formalisms and processes. The text presupposes a basic (undergraduate-level) understanding of mechanics, electrodynamics, and quantum mechanics. However, more specialized concepts in these fields are introduced and the reader is directed to appropriate references. While primarily benefiting users of x-ray light-sou...
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
Supersymmetric solutions for non-relativistic holography
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Blackett Laboratory, Imperial College, London (United Kingdom)]|[Institute for Mathematical Sciences, Imperial College, London (United Kingdom)
2009-01-15
We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z{>=}4 and z{>=}3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively. (orig.)
Mass of nonrelativistic meson from leading twist distribution amplitudes
Energy Technology Data Exchange (ETDEWEB)
Braguta, V. V., E-mail: braguta@mail.ru [Institute for High Energy Physics (Russian Federation)
2011-01-15
In this paper distribution amplitudes of pseudoscalar and vector nonrelativistic mesons are considered. Using equations of motion for the distribution amplitudes, relations are derived which allow one to calculate the masses of nonrelativistic pseudoscalar and vector meson if the leading twist distribution amplitudes are known. These relations can be also rewritten as relations between the masses of nonrelativistic mesons and infinite series of QCD operators, what can be considered as an exact version of Gremm-Kapustin relation in NRQCD.
Frederico, T; Pasquini, B; Salme', G
2009-01-01
The generalized parton distributions of the pion are studied within different light-front approaches for the quark-hadron and quark-photon vertices, exploring different kinematical regions in both the valence and non-valence sector. Moments of the generalized parton distributions which enter the definition of generalized form factors are also compared with recent lattice calculations.
Effective approach to non-relativistic quantum mechanics
Jacobs, David M
2015-01-01
Boundary conditions on non-relativistic wavefunctions are generally not completely constrained by the basic precepts of quantum mechanics, so understanding the set of possible self-adjoint extensions of the Hamiltonian is required. For real physical systems, non-trivial self-adjoint extensions have been used to model contact potentials when those interactions are expected a priori. However, they must be incorporated into the effective description of any quantum mechanical system in order to capture possible short-distance physics that does not decouple in the low energy limit. Here, an approach is described wherein an artificial boundary is inserted at an intermediate scale on which boundary conditions may encode short-distance effects that are hidden behind the boundary. Using this approach, an analysis is performed of the free particle, harmonic oscillator, and Coulomb potential in three dimensions. Requiring measurable quantities, such as spectra and cross sections, to be independent of this artificial bou...
The Thomas-Fermi Quark Model: Non-Relativistic Aspects
Liu, Quan
2012-01-01
Non-relativistic aspects of the Thomas-Fermi statistical quark model are developed. A review is given and our modified approach to spin in the model is explained. Our results are limited so far to two inequivalent simultaneous wave functions which can apply to multiple degenerate flavors. An explicit spin interaction is introduced, which requires the introduction of a generalized spin "flavor". Although the model is designed to be most reliable for many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of octet and decouplet baryons. The low energy fit allows us to investigate the six-quark doubly strange H-dibaryon state, possible 6 quark nucleon-nucleon resonances and flavor symmetric strange states of higher quark content.
A Signed Particle Formulation of Non-Relativistic Quantum Mechanics
Sellier, Jean Michel
2015-01-01
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the val...
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Nonrelativistic effective field theory for axions
Braaten, Eric; Mohapatra, Abhishek; Zhang, Hong
2016-10-01
Axions can be described by a relativistic field theory with a real scalar field ϕ whose self-interaction potential is a periodic function of ϕ . Low-energy axions, such as those produced in the early Universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field ψ whose effective potential is a function of ψ*ψ . We determine the coefficients in the expansion of the effective potential to fifth order in ψ*ψ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to truncate the expansion of the effective potential in powers of ψ*ψ , we develop a sequence of systematically improvable approximations to the effective potential that resum terms of all orders in ψ*ψ .
Thermal quantum electrodynamics of nonrelativistic charged fluids.
Buenzli, Pascal R; Martin, Philippe A; Ryser, Marc D
2007-04-01
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the r(-6) decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.
Thermal quantum electrodynamics of nonrelativistic charged fluids
Buenzli, Pascal R.; Martin, Philippe A.; Ryser, Marc D.
2007-04-01
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the r-6 decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.
Nonrelativistic Quantum Mechanics with Fundamental Environment
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Nonrelativistic Effective Field Theory for Axions
Braaten, Eric; Zhang, Hong
2016-01-01
Axions can be described by a relativistic field theory with a real scalar field $\\phi$ whose self-interaction potential is a periodic function of $\\phi$. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field $\\psi$ whose effective potential is a function of $\\psi^*\\psi$. We determine the coefficients in the expansion of the effective potential to fifth order in $\\psi^*\\psi$ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to expand the effective potential in powers of $\\psi^*\\psi$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in $\\psi^*\\psi$.
Mullah, Muhammad Abu Shadeque; Benedetti, Andrea
2016-11-01
Besides being mainly used for analyzing clustered or longitudinal data, generalized linear mixed models can also be used for smoothing via restricting changes in the fit at the knots in regression splines. The resulting models are usually called semiparametric mixed models (SPMMs). We investigate the effect of smoothing using SPMMs on the correlation and variance parameter estimates for serially correlated longitudinal normal, Poisson and binary data. Through simulations, we compare the performance of SPMMs to other simpler methods for estimating the nonlinear association such as fractional polynomials, and using a parametric nonlinear function. Simulation results suggest that, in general, the SPMMs recover the true curves very well and yield reasonable estimates of the correlation and variance parameters. However, for binary outcomes, SPMMs produce biased estimates of the variance parameters for high serially correlated data. We apply these methods to a dataset investigating the association between CD4 cell count and time since seroconversion for HIV infected men enrolled in the Multicenter AIDS Cohort Study.
New approach to nonrelativistic diffeomorphism invariance and its applications
Banerjee, Rabin
2015-01-01
A comprehensive account of a new structured algorithm for obtaining nonrelativistic diffeomorphism invariances in both space and spacetime by gauging the Galilean symmetry in a generic nonrelativistic field theoretical model is provided. % where the original (global) symmetry is localised. Various applications like the obtention of nonrelativistic diffeomorphism invariance, the introduction of Chern-Simons term and its role in fractional quantum Hall effect, induction of diffeomorphism in irrotational fluid model, abstraction of Newton-Cartan geometry and the emergence of Horava-Lifshitz gravity are discussed in details.
Abdelmadjid Maireche
2017-01-01
The modified theories of noncommutative quantum mechanics have engrossed much attention in the last decade, especially its application to the fundamental three equations: Schrödinger, Klein-Gordon and Dirac equations. In this contextual exploration, we further investigate for modified quadratic Yukawa potential plus Mie-type potential (MIQYM) in the framework of modified nonrelativistic Schrödinger equation (MSE) using generalization of Bopp’s shift method and standard perturbation theory ins...
Quantization of Interacting Non-Relativistic Open Strings using Extended Objects
Arias, P J; Fuenmayor, E; Leal, L; Leal, Lorenzo
2005-01-01
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model comprises open-strings interacting through a Kalb-Ramond field in four dimensions. It is shown that a consistent geometric-representation can be built using a scheme of ``surfaces and lines of Faraday'', provided that the coupling constant (the ``charge'' of the string) is quantized.
Nonrelativistic limit of solution of radial quasipotential equations
Energy Technology Data Exchange (ETDEWEB)
Minh, Vu.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1986-10-01
For the S-wave case, solutions of relativistic radial quasipotential equations that degenerate in the limit c ..-->.. infinity into the Jost solutions of the corresponding nonrelativistic radial Schrodinger equations are found.
Corrections to the Nonrelativistic Ground Energy of a Helium Atom
Institute of Scientific and Technical Information of China (English)
段一士; 刘玉孝; 张丽杰
2004-01-01
Considering the nuclear motion, we present the nonrelativistic ground energy of a helium atom by using a simple effective variational wavefunction with a flexible parameter k. Based on the result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338 a.u. With the relative error 0.00034%.
Holographic energy loss in non-relativistic backgrounds
Atashi, Mahdi; Farahbodnia, Mitra
2016-01-01
In this paper, we study some aspects of energy loss in non-relativistic theories from holography. We analyze the energy lost by a rotating heavy point particle along a circle of radius $l$ with angular velocity $\\omega$ in theories with general dynamical exponent $z$ and hyperscaling violation exponent $\\theta$. It is shown that this problem provides a novel perspective on the energy loss in such theories. A general computation at zero and finite temperature is done and it is shown that how the total energy loss rate depends non-trivially on two characteristic exponents $(z,\\theta)$. We find that at zero temperature there is a special radius $l_c$ where the energy loss is independent of different values of $(z,\\theta)$. Also, there is a crossover between a regime in which the energy loss is dominated by the linear drag force and by the radiation because of the acceleration of the rotating particle. We discover different behaviors at finite temperature case.
Estimating Cosmological Parameter Covariance
Taylor, Andy
2014-01-01
We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not coincide unless the data covariance is exactly known. For sampled data covariances, with Gaussian distributed data and parameters, the parameter covariance matrix estimated from the width of the likelihood has a Wishart distribution, from which we derive the mean and covariance. This mean is biased and we propose an unbiased estimator of the parameter covariance matrix. Comparing our analytic results to a numerical Wishart sampler of the data covariance matrix we find excellent agreement. An accurate ansatz for the mean parameter covariance for the peak scatter estimator is found, and we fit its covariance to our numerical analysis. The mean is again biased and we propose an unbiased estimator for the peak parameter covariance. For sampled data covariances the width estimat...
Covariant representations of subproduct systems
Viselter, Ami
2010-01-01
A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with finding conditions for a covariant representation of a \\emph{subproduct system} to extend to a $C^*$-representation of the Toeplitz algebra. This framework is much more general than the former. We are able to find sufficient conditions, and show that in important special cases, they are also necessary. Further results include the universality of the tensor algebra, dilations of completely contractive covariant representations, Wold decompositions and von Neumann inequalities.
Energy Technology Data Exchange (ETDEWEB)
Parvan, A.S. [Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, Bucharest (Romania); Moldova Academy of Sciences, Institute of Applied Physics, Chisinau (Moldova, Republic of)
2015-09-15
In the present paper, the Tsallis statistics in the grand canonical ensemble was reconsidered in a general form. The thermodynamic properties of the nonrelativistic ideal gas of hadrons in the grand canonical ensemble was studied numerically and analytically in a finite volume and the thermodynamic limit. It was proved that the Tsallis statistics in the grand canonical ensemble satisfies the requirements of the equilibrium thermodynamics in the thermodynamic limit if the thermodynamic potential is a homogeneous function of the first order with respect to the extensive variables of state of the system and the entropic variable z = 1/(q - 1) is an extensive variable of state. The equivalence of canonical, microcanonical and grand canonical ensembles for the nonrelativistic ideal gas of hadrons was demonstrated. (orig.)
Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation
Zenczykowski, Piotr
2009-01-01
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space ...
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
Li, Yi; Wu, Congjun
2012-02-01
The usual Landau level quantization, as demonstrated in the 2D quantum Hall effect, is crucially based on the planar structure. In this talk, we explore its 3D counterpart possessing the full 3D rotational symmetry as well as the time reversal symmetry. We construct the Landau level Hamiltonians in 3 and higher dimensional flat space for both relativistic and non-relativistic fermions. The 3D cases with integer fillings are Z2 topological insulators. The non-relativistic version describes spin-1/2 fermions coupling to the Aharonov-Casher SU(2) gauge field. This system exhibits flat Landau levels in which the orbital angular momentum and the spin are coupled with a fixed helicity. Each filled Landau level contributes one 2D helical Dirac Fermi surface at an open boundary, which demonstrates the Z2 topological nature. A natural generalization to Dirac fermions is found as a square root problem of the above non-relativistic version, which can also be viewed as the Dirac equation defined on the phase space. All these Landau level problems can be generalized to arbitrary high dimensions systematically. [4pt] [1] Yi Li and Congjun Wu, arXiv:1103.5422.[0pt] [2] Yi Li, Ken Intriligator, Yue Yu and Congjun Wu, arXiv:1108.5650.
Covariant Impulse Approximation for the study of the internal structure of composite particles
De Sanctis, M; Milanes, D A; Sandoval, C E; Sanctis, Maurizio De; Acero, Mario A.; Milanes, Diego A.; Sandoval, Carlos E.
2004-01-01
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse Approximation, which is needed for the study of high momentum transfer processes.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Energy Technology Data Exchange (ETDEWEB)
Gevorkyan, A. S., E-mail: g_ashot@sci.am [NAS of Armenia, Institute for Informatics and Automation Problems (Armenia)
2013-08-15
Spontaneous transitions between bound states of an atomic system, the 'Lamb Shift' of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations (fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schroedinger type and is defined on the extended space Double-Struck-Capital-R {sup 3} Circled-Times {Xi}{sup n}, where Double-Struck-Capital-R {sup 3} and {Xi}{sup n} are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Gevorkyan, A. S.
2013-08-01
Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger type and is defined on the extended space ℝ3⊗Ξ n , where ℝ3 and Ξ n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Characterization of informational completeness for covariant phase space observables
Kiukas, J.; Lahti, P.; Schultz, J.; Werner, R. F.
2012-10-01
In the nonrelativistic setting with finitely many canonical degrees of freedom, a shift-covariant phase space observable is uniquely characterized by a positive operator of trace one and, in turn, by the Fourier-Weyl transform of this operator. We study three properties of such observables, and characterize them in terms of the zero set of this transform. The first is informational completeness, for which it is necessary and sufficient that the zero set has dense complement. The second is a version of informational completeness for the Hilbert-Schmidt class, equivalent to the zero set being of measure zero, and the third, known as regularity, is equivalent to the zero set being empty. We give examples demonstrating that all three conditions are distinct. The three conditions are the special cases for p = 1, 2, ∞ of a more general notion of p-regularity defined as the norm density of the span of translates of the operator in the Schatten-p class. We show that the relation between zero sets and p-regularity can be mapped completely to the corresponding relation for functions in classical harmonic analysis.
Worldline construction of a covariant chiral kinetic theory
Mueller, Niklas; Venugopalan, Raju
2017-07-01
We discuss a novel worldline framework for computations of the chiral magnetic effect (CME) in ultrarelativistic heavy-ion collisions. Starting from the fermion determinant in the QCD effective action, we show explicitly how its real part can be expressed as a supersymmetric worldline action of spinning, colored, Grassmannian particles in background fields. Restricting ourselves for simplicity to spinning particles, we demonstrate how their constrained Hamiltonian dynamics arises for both massless and massive particles. In a semiclassical limit, this gives rise to the covariant generalization of the Bargmann-Michel-Telegdi equation; the derivation of the corresponding Wong equations for colored particles is straightforward. In a previous paper [N. Mueller and R. Venugopalan, arXiv:1701.03331.], we outlined how Berry's phase arises in a nonrelativistic adiabatic limit for massive particles. We extend the discussion here to systems with a finite chemical potential. We discuss a path integral formulation of the relative phase in the fermion determinant that places it on the same footing as the real part. We construct the corresponding anomalous worldline axial-vector current and show in detail how the chiral anomaly appears. Our work provides a systematic framework for a relativistic kinetic theory of chiral fermions in the fluctuating topological backgrounds that generate the CME in a deconfined quark-gluon plasma. We outline some further applications of this framework in many-body systems.
Covariant Projective Extensions
Institute of Scientific and Technical Information of China (English)
许天周; 梁洁
2003-01-01
@@ The theory of crossed products of C*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classicaltheories of covariance algebras, see, for instance [1-3].
Non-Relativistic Limit of the Dirac Equation
Ajaib, Muhammad Adeel
2016-01-01
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.
On the Origin of Gravitational Lorentz Covariance
Khoury, Justin; Tolley, Andrew J
2013-01-01
We provide evidence that general relativity is the unique spatially covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of general relativity, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector.
Nonrelativistic factorizable scattering theory of multicomponent Calogero-Sutherland model
Ahn, C; Nam, S; Ahn, Changrim; Lee, Kong Ju Bock; Nam, Soonkeon
1995-01-01
We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable S-matrix theory with SU(N)-invariance. We find complete solutions of the Yang-Baxter equations without implementing the crossing symmetry, and one of them is identified with the scattering amplitudes derived from the Schr\\"{o}dinger equation of the Calogero-Sutherland model. This particular solution is of interest in that it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations.
On the Failure of Multiconfiguration Methods in the Nonrelativistic Limit
Esteban, Maria J; Savin, Andreas
2009-01-01
The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp+pd configurations in the J=1 sector leads to a symmetry breaking phenomenon in the sense that the ground state is never an eigenvector of L^2 or S^2. We thereby complement and clarify some previous studies.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Geracie, Michael; Roberts, Matthew M
2015-01-01
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativisitic symmetries which supports massive matter fields. In particular, one can not impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativis...
A brief introduction to non-relativistic supergravity
Energy Technology Data Exchange (ETDEWEB)
Zojer, Thomas [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen (Netherlands)
2016-04-15
Non-relativistic geometries have received more attention lately. We review our attempts to construct supersymmetric extensions of this so-called Newton-Cartan geometry in three space-time dimensions. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale
Lane, Charles D
2016-01-01
When the Standard-Model Extension (SME) is applied in curved spacetime, the Lorentz-violation coefficients must depend on spacetime position. This work describes some of the consequences of this spacetime variation. We focus on effects that appear at a nonrelativistic scale and extract sensitivity of completed experiments to derivatives of SME coefficient fields.
Theory of non-relativistic three-particle scattering
Malfliet, R.; Ruijgrok, Th.
1967-01-01
A new method, using asymptotically stationary states, is developed to calculate the S-matrix for the scattering of a non-relativistic particle by the bound state of two other particles. For the scattering with breakup of this bound state, we obtain a simplified form of the Faddeev integral
Covariate-free and Covariate-dependent Reliability.
Bentler, Peter M
2016-12-01
Classical test theory reliability coefficients are said to be population specific. Reliability generalization, a meta-analysis method, is the main procedure for evaluating the stability of reliability coefficients across populations. A new approach is developed to evaluate the degree of invariance of reliability coefficients to population characteristics. Factor or common variance of a reliability measure is partitioned into parts that are, and are not, influenced by control variables, resulting in a partition of reliability into a covariate-dependent and a covariate-free part. The approach can be implemented in a single sample and can be applied to a variety of reliability coefficients.
Manifestly covariant electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Hillion, P. [Institut Henri Poincare' , Le Vesinet (France)
1999-03-01
The conventional relativistic formulation of electromagnetism is covariant under the full Lorentz group. But relativity requires covariance only under the proper Lorentz group and the authors present here the formalism covariant under the complex rotation group isomorphic to the proper Lorentz group. The authors discuss successively Maxwell's equations, constitutive relations and potential functions. A comparison is made with the usual formulation.
van Enk, S. J.
2013-05-01
The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined covariantly. More precisely, two Lorentz-invariant 2D surfaces in spacetime can be defined such that magnetic and electric field lines are determined, for any observer, by the intersection of those surfaces with spacelike hyperplanes. An instance of this type of field is constituted by the so-called Hopf-Rañada solutions of the source-free Maxwell equations, which have been studied because of their interesting topological properties, namely, linkage of their field lines. In order to describe both geometric and topological properties in a succinct manner, we employ the tools of geometric algebra (aka Clifford algebra) and use the Clebsch representation for the vector potential as well as the Euler representation for both magnetic and electric fields. This description is easily made covariant, thus allowing us to define electric and magnetic field lines covariantly in a compact geometric language. The definitions of field lines can be phrased in terms of 2D surfaces in space. We display those surfaces in different reference frames, showing how those surfaces change under Lorentz transformations while keeping their topological properties. As a byproduct we also obtain relations between optical helicity, optical chirality and generalizations thereof, and their conservation laws.
Covariant formulation of the governing equations of continuum mechanics in an Eulerian description
Schöberl, Markus; Schlacher, Kurt
2007-05-01
We present the balance relations for a continuum in the Eulerian formulation in a pure covariant fashion. Based on the analysis of nonrelativistic particle mechanics, we adapt the covariant description to the case of a continuum. The use of the covariant Nijenhuis differential as well as the splitting of the vertical configuration bundle are the key objects that allow a coordinate-free representation. We state the balance equations such that they are valid, also when time variant transformations are applied, which leads to a nontrivial space-time connection and a metric which explicitly depends on the time.
Geometric Representation of Interacting Non-Relativistic Open Strings using Extended Objects
Arias, P J; Fuenmayor, E; Leal, L
2013-01-01
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model consists of open-strings interacting through a Kalb-Ramond field in four dimensions. The geometric representation proposed uses lines and surfaces that can be interpreted as an extension of the picture of Faraday's lines of classical electromagnetism. This representation results to be consistent, provided the coupling constant (the "charge" of the string) is quantized. The Schr\\"odinger equation in this representation is also presented.
Cosmic Censorship Conjecture revisited: Covariantly
Hamid, Aymen I M; Maharaj, Sunil D
2014-01-01
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.
Criterion for stability of a special relativistically covariant dynamical system
Horwitz, L. P.; Zucker, D.
2017-03-01
We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the geometric method (GEM) developed for the analysis of nonrelativistic Hamiltonian systems to study the local stability of a relativistic Duffing oscillator. Poincaré plots of the simulated motion are consistent with the RGEM. We find a threshold for the external driving force required for chaotic behavior in the Minkowski spacetime.
Hubeny, Veronika E
2014-01-01
A recently explored interesting quantity in AdS/CFT, dubbed 'residual entropy', characterizes the amount of collective ignorance associated with either boundary observers restricted to finite time duration, or bulk observers who lack access to a certain spacetime region. However, the previously-proposed expression for this quantity involving variation of boundary entanglement entropy (subsequently renamed to 'differential entropy') works only in a severely restrictive context. We explain the key limitations, arguing that in general, differential entropy does not correspond to residual entropy. Given that the concept of residual entropy as collective ignorance transcends these limitations, we identify two correspondingly robust, covariantly-defined constructs: a 'strip wedge' associated with boundary observers and a 'rim wedge' associated with bulk observers. These causal sets are well-defined in arbitrary time-dependent asymptotically AdS spacetimes in any number of dimensions. We discuss their relation, spec...
Deriving covariant holographic entanglement
Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
2016-11-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Deriving covariant holographic entanglement
Dong, Xi; Rangamani, Mukund
2016-01-01
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Delayed Equation for Charged Rigid Nonrelativistic Ball
Vlasov, A A
2002-01-01
Simple expression for self-force acting on radiating rigid charged ball is derived (Sommerfeld ball). It is shown that appropriate delayed equation of motion has solutions in general differ from that for Sommerfeld sphere - there are no "radiationless" solutions, but there are oscillating without damping solutions though self-force has nonzero value.
Entanglement and mutual information in 2d nonrelativistic field theories
Hosseini, Seyed Morteza
2015-01-01
We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Fodor, Z; Katz, S D; Lellouch, L; Portelli, A; Szabo, K K; Toth, B C
2015-01-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Do non-relativistic neutrinos constitute the dark matter?
Nieuwenhuizen, T.M.
2009-01-01
The dark matter of the Abell 1689 Galaxy Cluster is modeled by thermal, non-relativistic gravitating fermions and its galaxies and X-ray gas by isothermal distributions. A fit yields a mass of h(70)(1/2) (12/(g) over bar)(1)/(4) 1.445(30) eV. A dark-matter fraction Omega(nu) = h(70)(-3/2) 0.1893(39)
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Energy Technology Data Exchange (ETDEWEB)
Fodor, Z. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich (Germany); Institute for Theoretical Physics, Eötvös University, H-1117 Budapest (Hungary); Hoelbling, C. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Katz, S.D. [Institute for Theoretical Physics, Eötvös University, H-1117 Budapest (Hungary); MTA-ELTE Lendület Lattice Gauge Theory Research Group, H-1117 Budapest (Hungary); Lellouch, L., E-mail: lellouch@cpt.univ-mrs.fr [CNRS, Aix-Marseille U., U. de Toulon, CPT, UMR 7332, F-13288, Marseille (France); Portelli, A. [School of Physics & Astronomy, University of Southampton, SO17 1BJ (United Kingdom); Szabo, K.K. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich (Germany); Toth, B.C. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany)
2016-04-10
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Directory of Open Access Journals (Sweden)
Z. Fodor
2016-04-01
Full Text Available Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Symmetries of nonrelativistic phase space and the structure of quark-lepton generation
Źenczykowski, Piotr
2009-06-01
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x2 + p2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.
Symmetries of nonrelativistic phase space and the structure of quark-lepton generation
Energy Technology Data Exchange (ETDEWEB)
Zenczykowski, Piotr, E-mail: piotr.zenczykowski@ifj.edu.p [Division of Theoretical Physics, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Krakow (Poland)
2009-06-01
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x{sup 2} + p{sup 2} constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.
Wachter, H
2007-01-01
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the braided line or the q-deformed Euclidean space in three dimensions. Hamiltonian operators for the free q-deformed particle in one as well as three dimensions are introduced. Plane waves as solutions to the corresponding Schroedinger equations are considered. Their completeness and orthonormality relations are written down. Expectation values of position and momentum observables are taken with respect to one-particle states and their time-dependence is discussed. A potential is added to the free-particle Hamiltonians and q-analogs of the Ehrenfest theorem are derived from the Heisenberg equations of motion. The conservation of probability is proved.
Symmetries and couplings of non-relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Festuccia, Guido [Department of Physics and Astronomy, Uppsala University,Lägerhyddsvägen 1, Uppsala (Sweden); Hansen, Dennis [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark); Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes,Université Libre de Bruxelles, C.P. 231, Brussels, 1050 (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark)
2016-11-08
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell’s equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a U(1) current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent z.
Symmetries and Couplings of Non-Relativistic Electrodynamics
Festuccia, Guido; Hartong, Jelle; Obers, Niels A
2016-01-01
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galile...
Covariant electromagnetic field lines
Hadad, Y.; Cohen, E.; Kaminer, I.; Elitzur, A. C.
2017-08-01
Faraday introduced electric field lines as a powerful tool for understanding the electric force, and these field lines are still used today in classrooms and textbooks teaching the basics of electromagnetism within the electrostatic limit. However, despite attempts at generalizing this concept beyond the electrostatic limit, such a fully relativistic field line theory still appears to be missing. In this work, we propose such a theory and define covariant electromagnetic field lines that naturally extend electric field lines to relativistic systems and general electromagnetic fields. We derive a closed-form formula for the field lines curvature in the vicinity of a charge, and show that it is related to the world line of the charge. This demonstrates how the kinematics of a charge can be derived from the geometry of the electromagnetic field lines. Such a theory may also provide new tools in modeling and analyzing electromagnetic phenomena, and may entail new insights regarding long-standing problems such as radiation-reaction and self-force. In particular, the electromagnetic field lines curvature has the attractive property of being non-singular everywhere, thus eliminating all self-field singularities without using renormalization techniques.
Bergshoeff, E.; Pope, C.N.; Stelle, K.S.
1990-01-01
We discuss the notion of higher-spin covariance in w∞ gravity. We show how a recently proposed covariant w∞ gravity action can be obtained from non-chiral w∞ gravity by making field redefinitions that introduce new gauge-field components with corresponding new gauge transformations.
,
2016-01-01
With Einstein's inertial motion (free-falling and non-rotating relative to gyroscopes), geodesics for non-relativistic particles can intersect repeatedly, allowing one to compute the space-time curvature $R^{\\hat{0} \\hat{0}}$ exactly. Einstein's $R^{\\hat{0} \\hat{0}}$ for strong gravitational fields and for relativistic source-matter is identical with the Newtonian expression for the relative radial acceleration of neighboring free-falling test-particles, spherically averaged.--- Einstein's field equations follow from Newtonian experiments, local Lorentz-covariance, and energy-momentum conservation combined with the Bianchi identity.
Δ - Δ resonance in the nonrelativistic quark model
Cvetič, M.; Golli, B.; Mankoč-Borštnik, N.; Rosina, M.
1980-06-01
The Δ - Δ resonance is treated in the nonrelativistic quark model. The trial wave function is a colour singlet including N-N, Δ - Δ and coloured baryon channels. The effective Δ - Δ potential is repulsive at all distances for T=0, S=1, L=0,2,4 while for T=3, S=0, L=0 and T=0, S=3, L=0 it has a minimum. The GCM calculation gives for the latter state the binding emergy ∼ -40 MeV.
Conservation of energy and momentum in nonrelativistic plasmas
Energy Technology Data Exchange (ETDEWEB)
Sugama, H.; Watanabe, T.-H. [National Institute for Fusion Science, Toki 509-5292 (Japan); Graduate University for Advanced Studies, Toki 509-5292 (Japan); Nunami, M. [National Institute for Fusion Science, Toki 509-5292 (Japan)
2013-02-15
Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampere system [Sugama, Phys. Plasmas 7, 466 (2000)]. The symmetric pressure tensor is obtained from modifying the asymmetric canonical pressure tensor with using the rotational symmetry of the action integral. Differences between the resultant conservation laws and those for the Vlasov-Maxwell system including the Maxwell displacement current are clarified. These results provide a useful basis for gyrokinetic conservation laws because gyrokinetic equations are derived as an approximation of the Vlasov-Poisson-Ampere system.
Non-relativistic Bondi–Metzner–Sachs algebra
Batlle, Carles; Delmastro, Diego; Gomis, Joaquim
2017-09-01
We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein–Gordon field.
On the question of symmetries in non-relativistic diffeomorphism invariant theories
Banerjee, Rabin; Mukherjee, Pradip
2016-01-01
Nonrelativistic diffeomorphism invariance has recently emerged as a powerful tool for investigating various phenomena. The flat limit of such an invariance which should yield the Galilean invariance is, surprisingly, riddled with ambiguities and anomalies. We show that our approach, based on Galilean gauge theory, resolves these shortcomings. As a spin-off, we provide a systematic and unique way of interpreting nonrelativistic diffeomorphism invariance and Galilean invariance as appropriate nonrelativistic limits of relativistic invariances in curved and flat backgrounds, respectively. The complementary role of flat and nonrelativistic limits is highlighted.
From Gauging Nonrelativistic Translations to N-Body Dynamics
Lukierski, J; Zakrzewski, W J
2001-01-01
We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge-invariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d\\times (d+1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d=2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. We describe the effective interaction of the d=2 N-particle problem and discuss its classical solution for N=2. The phase space Hamilt...
Haider, Md. Masum
2016-12-01
An attempt has been taken to find a general equation for degenerate pressure of Chandrasekhar and constants, by using which one can study nonrelativistic as well as ultra-relativistic cases instead of two different equations and constants. Using the general equation, ion-acoustic solitary and shock waves have been studied and compared, numerically and graphically, the two cases in same situation of electron-positron-ion plasmas. Korteweg-de Vries (KdV) and KdV-Barger equations have been derived as well as their solution to study the soliton and shock profiles, respectively.
Cotner, Eric
2016-09-01
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These boson stars are solitonic solutions to the Einstein-Klein-Gordon equations but may be approximated in the nonrelativistic regime with a coupled Schrödinger-Poisson system. General properties of single soliton states are derived, including the possibility of quartic self-interactions. Binary collisions between two solitons are then studied, and the effects of different mass ratios, relative phases, self-couplings, and separation distances are characterized, leading to an easy conceptual understanding of how these parameters affect the collision outcome in terms of conservation of energy. Applications to dark matter are discussed.
Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions
Lin, Chris L
2015-01-01
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in lower-dimensional systems. The potential appearance of a Jacobian $J$ due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the $J=1$ case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, $J=1$, is not natural, and the generalization to the case $J\
Frasinski, Leszek J.
2016-08-01
Recent technological advances in the generation of intense femtosecond pulses have made covariance mapping an attractive analytical technique. The laser pulses available are so intense that often thousands of ionisation and Coulomb explosion events will occur within each pulse. To understand the physics of these processes the photoelectrons and photoions need to be correlated, and covariance mapping is well suited for operating at the high counting rates of these laser sources. Partial covariance is particularly useful in experiments with x-ray free electron lasers, because it is capable of suppressing pulse fluctuation effects. A variety of covariance mapping methods is described: simple, partial (single- and multi-parameter), sliced, contingent and multi-dimensional. The relationship to coincidence techniques is discussed. Covariance mapping has been used in many areas of science and technology: inner-shell excitation and Auger decay, multiphoton and multielectron ionisation, time-of-flight and angle-resolved spectrometry, infrared spectroscopy, nuclear magnetic resonance imaging, stimulated Raman scattering, directional gamma ray sensing, welding diagnostics and brain connectivity studies (connectomics). This review gives practical advice for implementing the technique and interpreting the results, including its limitations and instrumental constraints. It also summarises recent theoretical studies, highlights unsolved problems and outlines a personal view on the most promising research directions.
Covariant Bardeen perturbation formalism
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
The covariate-adjusted frequency plot.
Holling, Heinz; Böhning, Walailuck; Böhning, Dankmar; Formann, Anton K
2016-04-01
Count data arise in numerous fields of interest. Analysis of these data frequently require distributional assumptions. Although the graphical display of a fitted model is straightforward in the univariate scenario, this becomes more complex if covariate information needs to be included into the model. Stratification is one way to proceed, but has its limitations if the covariate has many levels or the number of covariates is large. The article suggests a marginal method which works even in the case that all possible covariate combinations are different (i.e. no covariate combination occurs more than once). For each covariate combination the fitted model value is computed and then summed over the entire data set. The technique is quite general and works with all count distributional models as well as with all forms of covariate modelling. The article provides illustrations of the method for various situations and also shows that the proposed estimator as well as the empirical count frequency are consistent with respect to the same parameter.
Covariant canonical quantization
Energy Technology Data Exchange (ETDEWEB)
Hippel, G.M. von [University of Regina, Department of Physics, Regina, Saskatchewan (Canada); Wohlfarth, M.N.R. [Universitaet Hamburg, Institut fuer Theoretische Physik, Hamburg (Germany)
2006-09-15
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and we apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a ''first'' or pre-quantization within the framework of conventional QFT. (orig.)
Covariant canonical quantization
Von Hippel, G M; Hippel, Georg M. von; Wohlfarth, Mattias N.R.
2006-01-01
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. Covariant canonical quantization agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses.
Covariance Applications with Kiwi
Mattoon, C. M.; Brown, D.; Elliott, J. B.
2012-05-01
The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL) is developing a new tool, named `Kiwi', that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL) and large-scale Uncertainty Quantification (UQ) studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested using critical assemblies as a test case, and is being integrated into LLNL's quality assurance and benchmarking for nuclear data.
Covariance Applications with Kiwi
Directory of Open Access Journals (Sweden)
Elliott J.B.
2012-05-01
Full Text Available The Computational Nuclear Physics group at Lawrence Livermore National Laboratory (LLNL is developing a new tool, named ‘Kiwi’, that is intended as an interface between the covariance data increasingly available in major nuclear reaction libraries (including ENDF and ENDL and large-scale Uncertainty Quantification (UQ studies. Kiwi is designed to integrate smoothly into large UQ studies, using the covariance matrix to generate multiple variations of nuclear data. The code has been tested using critical assemblies as a test case, and is being integrated into LLNL's quality assurance and benchmarking for nuclear data.
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.
Differential Regularization of a Non-relativistic Anyon Model
Freedman, Daniel Z; Rius, N
1994-01-01
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\\phi$ with $\\lambda (\\phi {}^{*} \\phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\\phi {}^{*} \\phi {}^{*} \\phi \\phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions to $\\beta(\\lambda,e)$ vanish, and $\\beta(\\lambda,e)$ itself vanishes when the ``self-dual'' condition relating $\\lambda$ to the gauge coupling $e$ is imposed.
Nonrelativistic QED approach to the bound-electron g factor
Pachucki, K; Yerokhin, V A
2004-01-01
Within a systematic approach based on nonrelativistic quantum electrodynamics (NRQED), we derive the one-loop self-energy correction of order alpha (Zalpha)^4 to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha^2 (Zalpha)^4 ln[(Zalpha)^-2] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g factor measurements.
Nonrelativistic QED Approach to the Bound-Electron g Factor
Pachucki, Krzysztof; Jentschura, Ulrich D.; Yerokhin, Vladimir A.
2004-10-01
Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order α(Zα)4 to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order α2(Zα)4ln([(Zα)-2] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g-factor measurements.
Ion Injection at Non-relativistic Collisionless Shocks
Caprioli, Damiano; Spitkovsky, Anatoly
2014-01-01
We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for i...
Nonrelativistic QED expansion for the electron self-energy
Patkóš, V.; Šimsa, D.; Zamastil, J.
2017-01-01
The recently proposed relativistic multipole expansion (RME) of the self-energy effect suggests some observations on the nonrelativistic expansion of the effect. First, the nature of the series for the one-loop self-energy of an electron bound by the Coulomb field of the nucleus is clarified. It is shown that the expansion of the energy shift caused by the self-energy effect contains terms of the form α (Zα ) 7ln(Z α ) , α (Zα ) 8ln3(Z α ) , α (Zα ) 9ln2(Z α ) , α (Zα ) 10ln4(Z α ) , and so on. Here Z is the charge of the nucleus. The origin of these terms is traced back to the logarithmic divergence of the Dirac S -wave function at the origin. These terms eventually lead to breakdown of the nonrelativistic quantum electrodynamics approach. Second, at leading order relativistic multipole expansion requires an evaluation of the "extended Bethe logarithm" (EBL). When expanded in series in Z α EBL reduces at leading order to the ordinary Bethe logarithm. However, it is argued that it is both more accurate and easier to calculate the EBL than the ordinary Bethe logarithm. Both variants of the Bethe logarithm can be calculated by means of the pseudostate method. An improvement of this method is suggested. Finally, the contribution of the combined self-energy vacuum polarization contribution to the Lamb shift in muonic hydrogen for the 1 s -4 s and 2 p -4 p states by means of the EBL is calculated. For cases that had already been calculated the results reported here are more accurate than the previous ones.
Saltas, Ippocratis D
2016-01-01
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the non-flat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Galileon higher-derivative interactions in the effective action. These terms, previously unnoticed within standard, non-covariant frameworks, are not Planck suppressed. Unless tuned to be sub-dominant, their presence could have important implications for the classical and quantum phenomenology of the theory.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Using Analysis of Covariance (ANCOVA) with Fallible Covariates
Culpepper, Steven Andrew; Aguinis, Herman
2011-01-01
Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…
Using Analysis of Covariance (ANCOVA) with Fallible Covariates
Culpepper, Steven Andrew; Aguinis, Herman
2011-01-01
Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…
Chi, Zhiyi
2010-01-01
Two extensions of generalized linear models are considered. In the first one, response variables depend on multiple linear combinations of covariates. In the second one, only response variables are observed while the linear covariates are missing. We derive stochastic Lipschitz continuity results for the loss functions involved in the regression problems and apply them to get bounds on estimation error for Lasso. Multivariate comparison results on Rademacher complexity are obtained as tools to establish the stochastic Lipschitz continuity results.
Pinto, Sérgio Alexandre; Gross, Franz
2009-01-01
We present the first calculations of the electromagnetic form factors of $^3$He and $^3$H within the framework of the Covariant Spectator Theory (CST). This first exploratory study concentrates on the sensitivity of the form factors to the strength of the scalar meson-nucleon off-shell coupling, known from previous studies to have a strong influence on the three-body binding energy. Results presented here were obtained using the complete impulse approximation (CIA), which includes contributions of relativistic origin that appear as two-body corrections in a non-relativistic framework, such as "Z-graphs", but omits other two and three-body currents. We compare our results to non-relativistic calculations augmented by relativistic corrections of ${\\cal O}(v/c)^2$.
Energy Technology Data Exchange (ETDEWEB)
Pinto, Sérgio Alexandre; Stadler, Alfred; Gross, Franz
2009-05-01
We present the first calculations of the electromagnetic form factors of ^{3}He and ^{3}H within the framework of the Covariant Spectator Theory (CST). This first exploratory study concentrates on the sensitivity of the form factors to the strength of the scalar meson-nucleon off-shell coupling, known from previous studies to have a strong influence on the three-body binding energy. Results presented here were obtained using the complete impulse approximation (CIA), which includes contributions of relativistic origin that appear as two-body corrections in a non-relativistic framework, such as "Z-graphs," but omits other two and three-body currents. Finally, we compare our results to non-relativistic calculations augmented by relativistic corrections of O(v/c)^{2}.
A chiral covariant approach to $\\rho\\rho$ scattering
Gülmez, D; Oller, J A
2016-01-01
We analyze vector meson - vector meson scattering in a unitarized chiral theory based on a chiral covariant framework. We show that a pole assigned to the the scalar meson $f_0(1370)$ can be dynamically generated from the $\\rho\\rho$ interaction, while this is not the case for the tensor meson $f_2(1270)$ as found in earlier works. We show that the generation of the tensor state is untenable due to an artefact of the extreme non-relativistic kinematics used before. We further consider the effects arising from the coupling of channels with different orbital angular momenta. We suggest to use the formalism outlined here to obtain more reliable results for the dynamical generation of resonances in the vector-vector interaction.
Bottom mass from nonrelativistic sum rules at NNLL
Energy Technology Data Exchange (ETDEWEB)
Stahlhofen, Maximilian
2013-01-15
We report on a recent determination of the bottom quark mass from nonrelativistic (large-n) {Upsilon} sum rules with renormalization group improvement (RGI) at next-to-next-to-leading logarithmic (NNLL) order. The comparison to previous fixed-order analyses shows that the RGI computed in the vNRQCD framework leads to a substantial stabilization of the theoretical sum rule moments with respect to scale variations. A single moment fit (n=10) to the available experimental data yields M{sub b}{sup 1S}=4.755{+-}0.057{sub pert}{+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass. The quoted uncertainties refer to the perturbative error and the uncertainties associated with the strong coupling and the experimental input.
Non-Relativistic Anti-Snyder Model and Some Applications
Ching, Chee Leong; Ng, Wei Khim
2016-01-01
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigen solutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states due to the orthogonality of the polynomials and the maximum energy is truncated at the maximum n. Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti- Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit. By taking zero mass limit, we explore the motion of effective zero mass charged Fermions in Graphene like material and obtained a maximum bound of deformed parameter. Furthermore, we consider the modified energy dispersion relations and its...
Nonrelativistic anti-Snyder model and some applications
Ching, C. L.; Yeo, C. X.; Ng, W. K.
2017-01-01
In this paper, we examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states nmax due to the orthogonality of the polynomials and the maximum energy is truncated at nmax. Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit β → 0. By taking m → 0, we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter βmax. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.
Radiation of non-relativistic particle on a conducting sphere and a string of spheres
Shul'ga, N F; Larikova, E A
2016-01-01
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
Adorno, T C; Gitman, D M
2010-01-01
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $\\theta$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $\\theta$-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (\\`a la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the $\\theta$-modified Pauli equation. Then, we extract $\\theta$-modified interaction between a nonrelativistic spin and a magnetic field from the $\\theta$-modified Pauli equation and construct a $\\theta$-modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal EPR (Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which...
Adorno, T C; Gitman, D M
2010-01-01
We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $\\theta$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $\\theta$-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (\\`a la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the $\\theta$-modified Pauli equation. We extract $\\theta$-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a $\\theta$-modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal EPR (Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the...
Universality of Covariance Matrices
Pillai, Natesh S
2011-01-01
We prove the universality of covariance matrices of the form $H_{N \\times N} = {1 \\over N} \\tp{X}X$ where $[X]_{M \\times N}$ is a rectangular matrix with independent real valued entries $[x_{ij}]$ satisfying $\\E \\,x_{ij} = 0$ and $\\E \\,x^2_{ij} = {1 \\over M}$, $N, M\\to \\infty$. Furthermore it is assumed that these entries have sub-exponential tails. We will study the asymptotics in the regime $N/M = d_N \\in (0,\\infty), \\lim_{N\\to \\infty}d_N \
Notes on Cosmic Censorship Conjecture revisited: Covariantly
Hamid, Aymen I M; Maharaj, Sunil D
2016-01-01
In this paper we study the dynamics of the trapped region using a frame independent semi-tetrad covariant formalism for general Locally Rotationally Symmetric (LRS) class II spacetimes. We covariantly prove some important geometrical results for the apparent horizon, and state the necessary and sufficient conditions for a singularity to be locally naked. These conditions bring out, for the first time in a quantitative and transparent manner, the importance of the Weyl curvature in deforming and delaying the trapped region during continual gravitational collapse, making the central singularity locally visible.
Spatiotemporal noise covariance estimation from limited empirical magnetoencephalographic data
Energy Technology Data Exchange (ETDEWEB)
Jun, Sung C [MS-D454, Applied Modern Physics Group, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Plis, Sergey M [MS-D454, Applied Modern Physics Group, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Ranken, Doug M [MS-D454, Applied Modern Physics Group, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Schmidt, David M [MS-D454, Applied Modern Physics Group, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2006-11-07
The performance of parametric magnetoencephalography (MEG) and electroencephalography (EEG) source localization approaches can be degraded by the use of poor background noise covariance estimates. In general, estimation of the noise covariance for spatiotemporal analysis is difficult mainly due to the limited noise information available. Furthermore, its estimation requires a large amount of storage and a one-time but very large (and sometimes intractable) calculation or its inverse. To overcome these difficulties, noise covariance models consisting of one pair or a sum of multi-pairs of Kronecker products of spatial covariance and temporal covariance have been proposed. However, these approaches cannot be applied when the noise information is very limited, i.e., the amount of noise information is less than the degrees of freedom of the noise covariance models. A common example of this is when only averaged noise data are available for a limited prestimulus region (typically at most a few hundred milliseconds duration). For such cases, a diagonal spatiotemporal noise covariance model consisting of sensor variances with no spatial or temporal correlation has been the common choice for spatiotemporal analysis. In this work, we propose a different noise covariance model which consists of diagonal spatial noise covariance and Toeplitz temporal noise covariance. It can easily be estimated from limited noise information, and no time-consuming optimization and data-processing are required. Thus, it can be used as an alternative choice when one-pair or multi-pair noise covariance models cannot be estimated due to lack of noise information. To verify its capability we used Bayesian inference dipole analysis and a number of simulated and empirical datasets. We compared this covariance model with other existing covariance models such as conventional diagonal covariance, one-pair and multi-pair noise covariance models, when noise information is sufficient to estimate them. We
Earth Observing System Covariance Realism
Zaidi, Waqar H.; Hejduk, Matthew D.
2016-01-01
The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.
Nonrelativistic mean-field description of the deformation of Λ hypernuclei
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.
Golubovic, Leonardo; Knudsen, Steven
2017-01-01
We consider general problem of modeling the dynamics of objects sliding on moving strings. We introduce a powerful computational algorithm that can be used to investigate the dynamics of objects sliding along non-relativistic strings. We use the algorithm to numerically explore fundamental physics of sliding climbers on a unique class of dynamical systems, Rotating Space Elevators (RSE). Objects sliding along RSE strings do not require internal engines or propulsion to be transported from the Earth's surface into outer space. By extensive numerical simulations, we find that sliding climbers may display interesting non-linear dynamics exhibiting both quasi-periodic and chaotic states of motion. While our main interest in this study is in the climber dynamics on RSEs, our results for the dynamics of sliding object are of more general interest. In particular, we designed tools capable of dealing with strongly nonlinear phenomena involving moving strings of any kind, such as the chaotic dynamics of sliding climbers observed in our simulations.
Covariant Lyapunov vectors for rigid disk systems.
Bosetti, Hadrien; Posch, Harald A
2010-10-05
We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.
Kriging approach for the experimental cross-section covariances estimation
Directory of Open Access Journals (Sweden)
Garlaud A.
2013-03-01
Full Text Available In the classical use of a generalized χ2 to determine the evaluated cross section uncertainty, we need the covariance matrix of the experimental cross sections. The usual propagation error method to estimate the covariances is hardly usable and the lack of data prevents from using the direct empirical estimator. We propose in this paper to apply the kriging method which allows to estimate the covariances via the distances between the points and with some assumptions on the covariance matrix structure. All the results are illustrated with the 2555Mn nucleus measurements.
Bashir, M F
2012-01-01
Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those electromagnetic modes whose magnetic field perturbations are perpendicular to the ambient magneticeld, i.e.,B1 \\perp B0, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them and the O-mode are affected by thermal anisotropies, since they satisfy the required condition B1\\perpB0. By contrast, the perpendicular...
On the bilinear covariants associated to mass dimension one spinors
Energy Technology Data Exchange (ETDEWEB)
Silva, J.M.H. da; Villalobos, C.H.C.; Rogerio, R.J.B. [DFQ, UNESP, Guaratingueta, SP (Brazil); Scatena, E. [Universidade Federal de Santa Catarina-CEE, Blumenau, SC (Brazil)
2016-10-15
In this paper we approach the issue of Clifford algebra basis deformation, allowing for bilinear covariants associated to Elko spinors which satisfy the Fierz-Pauli-Kofink identities. We present a complete analysis of covariance, taking into account the involved dual structure associated to Elko spinors. Moreover, the possible generalizations to the recently presented new dual structure are performed. (orig.)
On the bilinear covariants associated to mass dimension one spinors
da Silva, J M Hoff; Rogerio, R J Bueno; Scatena, E
2016-01-01
In this paper we approach the issue of Clifford algebra basis deformation, allowing for bilinear covariants associated to Elko spinors which satisfy the Fierz-Pauli-Kofink identities. We present a complete analysis of covariance, taking into account the involved dual structure associated to Elko. Moreover, the possible generalizations to the recently presented new dual structure are performed.
Theory of Covariance Equivalent ARMAV Models of Civil Engineering Structures
DEFF Research Database (Denmark)
Andersen, P.; Brincker, Rune; Kirkegaard, Poul Henning
1996-01-01
In this paper the theoretical background for using covariance equivalent ARMAV models in modal analysis is discussed. It is shown how to obtain a covariance equivalent ARMA model for a univariate linear second order continous-time system excited by Gaussian white noise. This result is generalized...
Theory of Covariance Equivalent ARMAV Models of Civil Engineering Structures
DEFF Research Database (Denmark)
Andersen, P.; Brincker, Rune; Kirkegaard, Poul Henning
In this paper the theoretical background for using covariance equivalent ARMAV models in modal analysis is discussed. It is shown how to obtain a covariance equivalent ARMA model for a univariate linear second order continuous-time system excited by Gaussian white noise. This result is generalize...
Theory of Covariance Equivalent ARMAV Models of Civil Engineering Structures
DEFF Research Database (Denmark)
Andersen, P.; Brincker, Rune; Kirkegaard, Poul Henning
1996-01-01
In this paper the theoretical background for using covariance equivalent ARMAV models in modal analysis is discussed. It is shown how to obtain a covariance equivalent ARMA model for a univariate linear second order continous-time system excited by Gaussian white noise. This result is generalized...
Time as an Observable in Nonrelativistic Quantum Mechanics
Hahne, G. E.
2003-01-01
The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Saltas, Ippocratis D.; Vitagliano, Vincenzo
2017-05-01
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the nonflat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Galileon higher-derivative interactions in the effective action. These terms, previously unnoticed within standard, noncovariant frameworks, are not Planck suppressed. Unless tuned to be subdominant, their presence could have important implications for the classical and quantum phenomenology of the theory.
Covariant holographic entanglement negativity
Chaturvedi, Pankaj; Sengupta, Gautam
2016-01-01
We conjecture a holographic prescription for the covariant entanglement negativity of $d$-dimensional conformal field theories dual to non static bulk $AdS_{d+1}$ gravitational configurations in the framework of the $AdS/CFT$ correspondence. Application of our conjecture to a $AdS_3/CFT_2$ scenario involving bulk rotating BTZ black holes exactly reproduces the entanglement negativity of the corresponding $(1+1)$ dimensional conformal field theories and precisely captures the distillable quantum entanglement. Interestingly our conjecture for the scenario involving dual bulk extremal rotating BTZ black holes also accurately leads to the entanglement negativity for the chiral half of the corresponding $(1+1)$ dimensional conformal field theory at zero temperature.
de Brito, G P; Gomes, Y M P; Junior, J T Guaitolini; Nikoofard, V
2016-01-01
In this paper we introduce a modified covariant quantum algebra based in the so-called Quesne-Tkachuk algebra. By means of a deformation procedure we arrive at a class of higher derivative models of gravity. The study of the particle spectra of these models reveals an equivalence with the physical content of the well-known renormalizable and super-renormalizable higher derivative gravities. The particle spectrum exhibits the presence of spurious complex ghosts and, in light of this problem, we suggest an interesting interpretation in the context of minimal length theories. Also, a discussion regarding the non-relativistic potential energy is proposed.
Radiative decays of $1^{++}$ heavy mesons in the covariant light-front approach
Shi, Yan-Liang
2016-01-01
We calculate the predicted width for the radiative decay of a $1^{++}$ heavy meson via the channel $1^{++} \\to 1^{--} +\\gamma$ in the covariant light-front quark model. Specifically, we compute the decay widths for $\\chi_{c1}(1P) \\to J/\\psi + \\gamma$ and $\\chi_{b1}(nP) \\to \\Upsilon(n'S) + \\gamma$. The results are compared with experimental data and with predictions from calculations based on nonrelativistic models and their extensions to include relativistic effects.
Bayes linear covariance matrix adjustment
Wilkinson, Darren J
1995-01-01
In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be a...
Continuity properties of the semi-group and its integral kernel in non-relativistic QED
Matte, Oliver
2016-07-01
Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J. S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued Lp-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostatic potentials and the actual assumptions on the model are general enough to cover the Nelson model as well. As a corollary, we obtain some new pointwise exponential decay and continuity results on elements of low-energetic spectral subspaces of atoms or molecules that also take spin into account. In a simpler situation where spin is neglected, we explain how to verify the joint continuity of positive ground state eigenvectors with respect to spatial coordinates and model parameters. There are no smallness assumptions imposed on any model parameter.
Classical and quantum mechanics of the nonrelativistic Snyder model in curved space
Mignemi, S
2011-01-01
The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales beside the speed of light, and is invariant under the action of the de Sitter group. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). We discuss the classical and the quantum mechanics of a free particle and of an oscillator in this framework. In analogy with the flat case, the properties of the SdS and aSdS model are rather different. In the SdS case, a lower bound on the localization in position and momentum space exists, which does not arise in the aSdS model. In both cases the energy of the harmonic oscillator acquires a dependence on the frequency, but the quantum mechanical aSdS oscillator admits only a finite numb...
Fu, X.; Waters, T.; Gary, S. P.
2014-12-01
Collisionless space plasmas often deviate from Maxwellian-like velocity distributions. To study kinetic waves and instabilities in such plasmas, the dispersion relation, which depends on the velocity distribution, needs to be solved numerically. Most current dispersion solvers (e.g. WHAMP) take advantage of mathematical properties of the Gaussian (or generalized Lorentzian) function, and assume that the velocity distributions can be modeled by a combination of several drift-Maxwellian (or drift-Lorentzian) components. In this study we are developing a kinetic dispersion solver that admits nearly arbitrary non-relativistic parallel velocity distributions. A key part of any dispersion solver is the evaluation of a Hilbert transform of the velocity distribution function and its derivative along Landau contours. Our new solver builds upon a recent method to compute the Hilbert transform accurately and efficiently using the fast Fourier transform, while simultaneously treating the singularities arising from resonances analytically. We have benchmarked our new solver against other codes dealing with Maxwellian distributions. As an example usage of our code, we will show results for several instabilities that occur for electron velocity distributions observed in the solar wind.
Institute of Scientific and Technical Information of China (English)
LUO Xiao-hua; WU Mu-ying; HE Wei; SHAO Ming-zhu; LUO Shi-yu
2011-01-01
Under classical mechanics, the general equation of particle motion in the periodic field is derived. In the dampless case, the existence possibility of the higher-order harmonic radiation is explored by using Bessel function expansion of a generalized trigonometrical function and the multi-scale method. In the damping case, the critical properties and a chaotic behavior are discussed by the Melnikov method. The results show that the use of a higher-order harmonic radiation of non-relativistic particles as a short-wavelength laser source is perfectly possible, and the system's critical condition is related to its parameters. Only by adjusting parameters suitablely, the stable higher-order harmonic radiation with bigger intensity can be obtained.
Relativistic and non-relativistic solitons in plasmas
Barman, Satyendra Nath
This thesis entitled as "Relativistic and Non-relativistic Solitons in Plasmas" is the embodiment of a number of investigations related to the formation of ion-acoustic solitary waves in plasmas under various physical situations. The whole work of the thesis is devoted to the studies of solitary waves in cold and warm collisionless magnetized or unmagnetized plasmas with or without relativistic effect. To analyze the formation of solitary waves in all our models of plasmas, we have employed two established methods namely - reductive perturbation method to deduce the Korteweg-de Vries (KdV) equation, the solutions of which represent the important but near exact characteristic concepts of soliton-physics. Next, the pseudopotential method to deduce the energy integral with total nonlinearity in the coupling process for exact characteristic results of solitons has been incorporated. In Chapter 1, a brief description of plasma in nature and laboratory and its generation are outlined elegantly. The nonlinear differential equations to characterize solitary waves and the relevant but important methods of solutions have been mentioned in this chapter. The formation of solitary waves in unmagnetized and magnetized plasmas, and in relativistic plasmas has been described through mathematical entity. Applications of plasmas in different fields are also put forwarded briefly showing its importance. The study of plasmas as they naturally occur in the universe encompasses number of topics including sun's corona, solar wind, planetary magnetospheres, ionospheres, auroras, cosmic rays and radiation. The study of space weather to understand the universe, communications and the activities of weather satellites are some useful areas of space plasma physics. The surface cleaning, sterilization of food and medical appliances, killing of bacteria on various surfaces, destroying of viruses, fungi, spores and plasma coating in industrial instruments ( like computers) are some of the fields
Institute of Scientific and Technical Information of China (English)
樊华; 山秀明; 任勇; 袁坚
2011-01-01
neglects the random variations in the controlled TCP flows. This paper aims at revealing the un-negligible influence from such random variations to the system stability. Using TCP/RED（TCP flows with random early detection） as an example, based on the stochastic differential equations of the system, the system is converted into a multi-dimensional linear time-invariant system with mixed additive and multiplicative noises by linearization at the equilibrium point. Then, generalized TCP flow control equations for continuous-time and discrete-time cases respectively are given, which are the first-degree time-invariant stochastic differential or difference equations with multi-noise-inputs. After that, the covariance matrix equation for such generalized system is derived; and based on this matrix equation, the sufficient and necessary condition when the covariance matrix has an asymptotically stable limit is presented, together with the expression of this limit. In engineering design, this condition can be regarded as a substitute criterion for estimating the motion domain. Finally, this general condition is applied to a specific example for demonstrating the change of the stability range when the stability of covariance is considered. Moreover, the results in this paper can be extended to the nonlinear system or time-varying system when treated by similar methods used in deterministic cases.
Revisiting radiative decays of $1^{+-}$ heavy quarkonia in the covariant light-front approach
Shi, Yan-Liang
2016-01-01
We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q \\bar Q$ meson via the channel $1^{+-} \\to 0^{-+} +\\gamma$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy quark mass and wavefunction structure parameter. We analyze the specific decays $h_{c}(1P) \\to \\eta_{c}(1S) + \\gamma$ and $h_{b}(1P) \\to \\eta_{b}(1S) + \\gamma$. We compare our results with experimental data and with other theoretical predictions from calculations based on non-relativistic models and their extensions to include relativistic effects, finding reasonable agreement.
Revisiting radiative decays of 1{sup +-} heavy quarkonia in the covariant light-front approach
Energy Technology Data Exchange (ETDEWEB)
Shi, Yan-Liang [Stony Brook University, C. N. Yang Institute for Theoretical Physics, Stony Brook, NY (United States)
2017-04-15
We revisit the calculation of the width for the radiative decay of a 1{sup +-} heavy Q anti Q meson via the channel 1{sup +-} → 0{sup -+}+γ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy-quark mass and wave function structure parameter. We analyze the specific decays h{sub c}(1P) → η{sub c}(1S) + γ and h{sub b}(1P) → η{sub b}(1S) + γ. We compare our results with experimental data and with other theoretical predictions from calculations based on non-relativistic models and their extensions to include relativistic effects, finding reasonable agreement. (orig.)
Dirac Monopole from Lorentz Symmetry in N-Dimensions: II. The Generalized Monopole
Land, M
2006-01-01
In a previous paper, we found an extension of the N-dimensional Lorentz generators that partially restores the closed operator algebra in the presence of a Maxwell field, and is conserved under system evolution. Generalizing the construction found by Berard, Grandati, Lages and Mohrbach for the angular momentum operators in the O(3)-invariant nonrelativistic case, we showed that the construction can be maximally satisfied in a three dimensional subspace of the full Minkowski space; this subspace can be chosen to describe either the O(3)-invariant space sector, or an O(2,1)-invariant restriction of spacetime. When the O(3)-invariant subspace is selected, the field solution reduces to the Dirac monopole field found in the nonrelativistic case. For the O(2,1)-invariant subspace, the Maxwell field can be associated with a Coulomb-like potential on spacetime, similar to that used by Horwitz and Arshansky to obtain a covariant generalization of the hydrogen-like bound state. In this paper we elaborate on the genera...
Some asymptotic properties of kriging when the covariance function is misspecified
Energy Technology Data Exchange (ETDEWEB)
Stein, M.L.; Handcock, M.S.
1989-02-01
The impact of using an incorrect covariance function of kriging predictors is investigated. Results of Stein (1988) show that the impact on the kriging predictor from not using the correct covariance function is asymptotically negligible as the number of observations increases if the covariance function used is compatible with the actual covariance function on the region of interest R. The definition and some properties of compatibility of covariance functions are given. The compatibility of generalized covariances also is defined. Compatibility supports the intuitively sensible concept that usually only the behavior near the origin of the covariance function is critical for purposes of kriging. However, the commonly used spherical covariance function is an exception: observations at a distance near the range of a spherical covariance function can have a nonnegligible effect on kriging predictors for three-dimensional processes. Finally, a comparison is made with the perturbation approach of Diamond and Armstrong (1984) and some observations of Warnes (1986) are clarified.
Adaptive Covariance Estimation with model selection
Biscay, Rolando; Loubes, Jean-Michel
2012-01-01
We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud.
Superfield quantization in Sp(2) covariant formalism
Lavrov, P M
2001-01-01
The rules of the superfield Sp(2) covariant quantization of the arbitrary gauge theories for the case of the introduction of the gauging with the derivative equations for the gauge functional are generalized. The possibilities of realization of the expanded anti-brackets are considered and it is shown, that only one of the realizations is compatible with the transformations of the expanded BRST-symmetry in the form of super translations along the Grassmann superspace coordinates
Are non-relativistic neutrinos the dark matter particles?
Nieuwenhuizen, Theo M.
2010-06-01
. Thereby the spead up the intracluster gas to virial speeds of 10 keV, which causes reionization without assistance of heavy stars. Within the analysis, the baryons are poor tracers of the dark matter density. This work is described in Theo M. Nieuwenhuizen, Do non-relativistic neutrinos constitute the dark matter? Europhysics Letters 86, 59001 (2009). This text of this paper is an update of this work. Structure formation is presently believed to need cold dark matter. However, hydrodynamics alone may explain baryonic clustering without this trigger. Th. M. Nieuwenhuizen, C. H. Gibson and R. E. Schild, Gravitational hydrodynamics of large scale structure formation, Europhysics Letters 2009, to appear.
Physical stress, mass, and energy for non-relativistic spinful matter
Geracie, Michael; Roberts, Matthew M
2016-01-01
For theories of relativistic matter fields with spin there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.
Energy Technology Data Exchange (ETDEWEB)
Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi [Department of Electrophysics, National Chiao Tung University,1001 University Street, Hsinchu, ROC (China)
2016-05-31
We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s−t and t−u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Lai, Sheng-Hong; Yang, Yi
2016-01-01
We review and extend high energy string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s-t and t-u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one leading trojectory string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi
2016-05-01
We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s- t and t- u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Newton law in covariant unimodular $F(R)$ gravity
Nojiri, S; Oikonomou, V K
2016-01-01
We propose a covariant ghost-free unimodular $F(R)$ gravity theory, which contains a three-form field and study its structure using the analogy of the proposed theory with a quantum system which describes a charged particle in uniform magnetic field. Newton's law in non-covariant unimodular $F(R)$ gravity as well as in unimodular Einstein gravity is derived and it is shown to be just the same as in General Relativity. The derivation of Newton's law in covariant unimodular $F(R)$ gravity shows that it is modified precisely in the same way as in the ordinary $F(R)$ theory. We also demonstrate that the cosmology of a Friedmann-Robertson-Walker background, is equivalent in the non-covariant and covariant formulations of unimodular $F(R)$ theory.
Beneke, M; Ruiz-Femenia, P
2014-01-01
This paper concludes the presentation of the non-relativistic effective field theory formalism designed to calculate the radiative corrections that enhance the pair-annihilation cross sections of slowly moving neutralinos and charginos within the general minimal supersymmetric standard model (MSSM). While papers I and II focused on the computation of the tree-level annihilation rates that feed into the short-distance part, here we describe in detail the method to obtain the Sommerfeld factors that contain the enhanced long-distance corrections. This includes the computation of the potential interactions in the MSSM, which are provided in compact analytic form, and a novel solution of the multi-state Schr\\"odinger equation that is free from the numerical instabilities generated by large mass splittings between the scattering states. Our results allow for a precise computation of the MSSM neutralino dark matter relic abundance and pair-annihilation rates in the present Universe, when Sommerfeld enhancements are...
Cotner, Eric
2016-01-01
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These boson stars are solitonic solutions to the Einstein-Klein-Gordon equations, but may be approximated in the non-relativistic regime with a coupled Schr\\"odinger-Poisson system. General properties of single soliton states are derived, including the possibility of quartic self-interactions. Binary collisions between two solitons are then studied, and the effects of different mass ratios, relative phases, self-couplings, and separation distances are characterized, leading to an easy conceptual understanding of how these parameters affect the collision outcome in terms of conservation of energy. Applications to dark matter are discussed.
The covariant description of field lines: application to linked beams of light
van Enk, S J
2013-01-01
The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain {\\em geometric} properties, field lines can be defined covariantly. More precisely, two Lorentz-invariant 2D surfaces in spacetime can be defined such that magnetic and electric field lines are determined, for any observer, by the intersection of those surfaces with spacelike hyperplanes. An instance of this type of field is constituted by the so-called Hopf-Ranada solutions of the source-free Maxwell equations, which have been studied because of their interesting topological properties, namely, linkage of their field lines. In order to describe both geometric and topological properties in a succinct manner, we employ the tools of Geometric Algebra (aka Clifford Algebra) and use the Clebsch representation for the vector potential as well as the Euler representation for both magnetic and electric fields. This description is easily made covariant, thus allowing us to de...
Energy Technology Data Exchange (ETDEWEB)
Rehman, M. A.; Qureshi, M. N. S. [Department of Physics, GC University, Kachery Road, Lahore 54000 (Pakistan); Shah, H. A. [Department of Physics, Forman Christian College, Ferozepur Road, Lahore 54600 (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shehzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-10-15
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
Covariant Quantum Gravity with Continuous Quantum Geometry I: Covariant Hamiltonian Framework
Pilc, Marián
2016-01-01
The first part of the series is devoted to the formulation of the Einstein-Cartan Theory within the covariant hamiltonian framework. In the first section the general multisymplectic approach is revised and the notion of the d-jet bundles is introduced. Since the whole Standard Model Lagrangian (including gravity) can be written as the functional of the forms, the structure of the d-jet bundles is more appropriate for the covariant hamiltonian analysis than the standard jet bundle approach. The definition of the local covariant Poisson bracket on the space of covariant observables is recalled. The main goal of the work is to show that the gauge group of the Einstein-Cartan theory is given by the semidirect product of the local Lorentz group and the group of spacetime diffeomorphisms. Vanishing of the integral generators of the gauge group is equivalent to equations of motion of the Einstein-Cartan theory and the local covariant algebra generated by Noether's currents is closed Lie algebra.
A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We formulate the general relativistic force-free electrodynamics in a new 3+1 language. In this formulation, when we have properly defined electric and magnetic fields, the covariant Maxwell equations could be cast in the traditional form with new vacuum con stitutive constraint equations. The fundamental equation governing a stationary, axisymmet ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3+1 system of Thorne and MacDonald, the new system of 3+1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applications in flat spacetime. We investigate its application to disk wind, black hole magnetosphere and solar physics in both flat and curved spacetime.
Covariant Quantization of CPT-violating Photons
Colladay, D; Noordmans, J P; Potting, R
2016-01-01
We perform the covariant canonical quantization of the CPT- and Lorentz-symmetry-violating photon sector of the minimal Standard-Model Extension, which contains a general (timelike, lightlike, or spacelike) fixed background tensor $k_{AF}^\\mu$. Well-known stability issues, arising from complex-valued energy states, are solved by introducing a small photon mass, orders of magnitude below current experimental bounds. We explicitly construct a covariant basis of polarization vectors, in which the photon field can be expanded. We proceed to derive the Feynman propagator and show that the theory is microcausal. Despite the occurrence of negative energies and vacuum-Cherenkov radiation, we do not find any runaway stability issues, because the energy remains bounded from below. An important observation is that the ordering of the roots of the dispersion relations is the same in any observer frame, which allows for a frame-independent condition that selects the correct branch of the dispersion relation. This turns ou...
Light Fermion Finite Mass Effects in Non-relativistic Bound States
Eiras, D; Eiras, Dolors; Soto, Joan
2000-01-01
We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, \\Upsilon (1s) and t\\bar{t} production near threshold are briefly discussed.
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Energy Technology Data Exchange (ETDEWEB)
Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)
2016-03-15
We find an exact formula for the thermally averaged cross section times the relative velocity left angle σv{sub rel} right angle with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at x = m/T >> 1 directly gives the nonrelativistic limit of left angle σv{sub rel} right angle, which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section σ(s) in powers of the nonrelativistic relative velocity vr. We show the correct invariant procedure that gives the nonrelativistic average left angle σv{sub rel} right angle {sub nr} coinciding with the large x expansion of left angle σv{sub rel} right angle in the comoving frame. We explicitly formulate flux, cross section, thermal average, collision integral of the Boltzmann equation in an invariant way using the true relativistic relative v{sub rel}, showing the uselessness of the Moeller velocity and further elucidating the conceptual and numerical inconsistencies related with its use. (orig.)
Cannoni, Mirco
2015-01-01
We find an exact formula for the thermally averaged cross section times the relative velocity $\\langle \\sigma v_{\\text{rel}} \\rangle$ with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at $x=m/T\\gg 1$ directly gives the nonrelativistic limit of $\\langle \\sigma v_{\\text{rel}}\\rangle$ which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section $\\sigma(s)$ in powers of the nonrelativistic relative velocity $v_r$. We show the correct invariant procedure that gives the nonrelativistic average $\\langle \\sigma_{nr} v_r \\rangle_{nr}$ coinciding with the large $x$ expansion of $\\langle \\sigma v_{\\text{rel}}\\rangle$ in the comoving frame. We explicitly formulate flux, cross section, thermal aver...
On the Theory of Resonances in Non-Relativistic QED and Related Models
DEFF Research Database (Denmark)
Abou Salem, Walid K.; Faupin, Jeremy; Froehlich, Juerg;
We study the mathematical theory of quantum resonances in the standard model of non-relativistic QED and in Nelson's model. In particular, we estimate the survival probability of metastable states corresponding to quantum resonances and relate the resonances to poles of an analytic continuation...
Jamei, Masoud; Dickinson, Gemma L; Rostami-Hodjegan, Amin
2009-01-01
An increasing number of failures in clinical stages of drug development have been related to the effects of candidate drugs in a sub-group of patients rather than the 'average' person. Expectation of extreme effects or lack of therapeutic effects in some subgroups following administration of similar doses requires a full understanding of the issue of variability and the importance of identifying covariates that determine the exposure to the drug candidates in each individual. In any drug development program the earlier these covariates are known the better. An important component of the drive to decrease this failure rate in drug development involves attempts to use physiologically-based pharmacokinetics 'bottom-up' modeling and simulation to optimize molecular features with respect to the absorption, distribution, metabolism and elimination (ADME) processes. The key element of this approach is the separation of information on the system (i.e. human body) from that of the drug (e.g. physicochemical characteristics determining permeability through membranes, partitioning to tissues, binding to plasma proteins or affinities toward certain enzymes and transporter proteins) and the study design (e.g. dose, route and frequency of administration, concomitant drugs and food). In this review, the classical 'top-down' approach in covariate recognition is compared with the 'bottom-up' paradigm. The determinants and sources of inter-individual variability in different stages of drug absorption, distribution, metabolism and excretion are discussed in detail. Further, the commonly known tools for simulating ADME properties are introduced.
Some covariance models based on normal scale mixtures
Schlather, Martin
2011-01-01
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new class is described that merges and generalizes various models presented in the literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97 (2002) 590--600) and Stein (Nonstationary spatial covariance functions (2005) Univ. Chicago). Furthermore, new models and a multivariate extension are introduced.
Web Tool for Constructing a Covariance Matrix from EXFOR Uncertainties
Directory of Open Access Journals (Sweden)
Zerkin V.
2012-05-01
Full Text Available The experimental nuclear reaction database EXFOR contains almost no covariance data because most experimentalists provide experimental data only with uncertainties. With the tool described here a user can construct an experimental covariance matrix from uncertainties using general assumptions when uncertainty information given in EXFOR is poor (or even absent. The tool is publically available in the IAEA EXFOR Web retrieval system [1].
Energy Technology Data Exchange (ETDEWEB)
Pang, Yang [Columbia Univ., New York, NY (United States)]|[Brookhaven National Labs., Upton, NY (United States)
1997-09-22
Many phenomenological models for relativistic heavy ion collisions share a common framework - the relativistic Boltzmann equations. Within this framework, a nucleus-nucleus collision is described by the evolution of phase-space distributions of several species of particles. The equations can be effectively solved with the cascade algorithm by sampling each phase-space distribution with points, i.e. {delta}-functions, and by treating the interaction terms as collisions of these points. In between collisions, each point travels on a straight line trajectory. In most implementations of the cascade algorithm, each physical particle, e.g. a hadron or a quark, is often represented by one point. Thus, the cross-section for a collision of two points is just the cross-section of the physical particles, which can be quite large compared to the local density of the system. For an ultra-relativistic nucleus-nucleus collision, this could lead to a large violation of the Lorentz invariance. By using the invariance property of the Boltzmann equation under a scale transformation, a Lorentz invariant cascade algorithm can be obtained. The General Cascade Program - GCP - is a tool for solving the relativistic Boltzmann equation with any number of particle species and very general interactions with the cascade algorithm.
Calcul Stochastique Covariant à Sauts & Calcul Stochastique à Sauts Covariants
Maillard-Teyssier, Laurence
2003-01-01
We propose a stochastic covariant calculus forcàdlàg semimartingales in the tangent bundle $TM$ over a manifold $M$. A connection on $M$ allows us to define an intrinsic derivative ofa $C^1$ curve $(Y_t)$ in $TM$, the covariantderivative. More precisely, it is the derivative of$(Y_t)$ seen in a frame moving parallelly along its projection curve$(x_t)$ on $M$. With the transfer principle, Norris defined thestochastic covariant integration along a continuous semimartingale in$TM$. We describe t...
Development of covariance capabilities in EMPIRE code
Energy Technology Data Exchange (ETDEWEB)
Herman,M.; Pigni, M.T.; Oblozinsky, P.; Mughabghab, S.F.; Mattoon, C.M.; Capote, R.; Cho, Young-Sik; Trkov, A.
2008-06-24
The nuclear reaction code EMPIRE has been extended to provide evaluation capabilities for neutron cross section covariances in the thermal, resolved resonance, unresolved resonance and fast neutron regions. The Atlas of Neutron Resonances by Mughabghab is used as a primary source of information on uncertainties at low energies. Care is taken to ensure consistency among the resonance parameter uncertainties and those for thermal cross sections. The resulting resonance parameter covariances are formatted in the ENDF-6 File 32. In the fast neutron range our methodology is based on model calculations with the code EMPIRE combined with experimental data through several available approaches. The model-based covariances can be obtained using deterministic (Kalman) or stochastic (Monte Carlo) propagation of model parameter uncertainties. We show that these two procedures yield comparable results. The Kalman filter and/or the generalized least square fitting procedures are employed to incorporate experimental information. We compare the two approaches analyzing results for the major reaction channels on {sup 89}Y. We also discuss a long-standing issue of unreasonably low uncertainties and link it to the rigidity of the model.
Levy Matrices and Financial Covariances
Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail
2003-10-01
In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.
Covariance of maximum likelihood evolutionary distances between sequences aligned pairwise.
Dessimoz, Christophe; Gil, Manuel
2008-06-23
The estimation of a distance between two biological sequences is a fundamental process in molecular evolution. It is usually performed by maximum likelihood (ML) on characters aligned either pairwise or jointly in a multiple sequence alignment (MSA). Estimators for the covariance of pairs from an MSA are known, but we are not aware of any solution for cases of pairs aligned independently. In large-scale analyses, it may be too costly to compute MSAs every time distances must be compared, and therefore a covariance estimator for distances estimated from pairs aligned independently is desirable. Knowledge of covariances improves any process that compares or combines distances, such as in generalized least-squares phylogenetic tree building, orthology inference, or lateral gene transfer detection. In this paper, we introduce an estimator for the covariance of distances from sequences aligned pairwise. Its performance is analyzed through extensive Monte Carlo simulations, and compared to the well-known variance estimator of ML distances. Our covariance estimator can be used together with the ML variance estimator to form covariance matrices. The estimator performs similarly to the ML variance estimator. In particular, it shows no sign of bias when sequence divergence is below 150 PAM units (i.e. above ~29% expected sequence identity). Above that distance, the covariances tend to be underestimated, but then ML variances are also underestimated.
Covariant Thermodynamics and Relativity
Lopez-Monsalvo, C S
2011-01-01
This thesis deals with the dynamics of irreversible processes within the context of the general theory of relativity. In particular, we address the problem of the 'infinite' speed of propagation of thermal disturbances in a dissipative fluid. The present work builds on the multi-fluid variational approach to relativistic dissipation, pioneered by Carter, and provides a dynamical theory of heat conduction. The novel property of such approach is the thermodynamic interpretation associated with a two-fluid system whose constituents are matter and entropy. The dynamics of this model leads to a relativistic generalisation of the Cattaneo equation; the constitutive relation for causal heat transport. A comparison with the Israel and Stewart model is presented and its equivalence is shown. This discussion provides new insights into the not-well understood definition of a non-equilibrium temperature. The variational approach to heat conduction presented in this thesis constitutes a mathematically promising formalism ...
Szekeres models: a covariant approach
Apostolopoulos, Pantelis S
2016-01-01
We exploit the 1+1+2 formalism to covariantly describe the inhomogeneous and anisotropic Szekeres models. It is shown that an \\emph{average scale length} can be defined \\emph{covariantly} which satisfies a 2d equation of motion driven from the \\emph{effective gravitational mass} (EGM) contained in the dust cloud. The contributions to the EGM are encoded to the energy density of the dust fluid and the free gravitational field $E_{ab}$. In addition the notions of the Apparent and Absolute Apparent Horizons are briefly discussed and we give an alternative gauge-invariant form to define them in terms of the kinematical variables of the spacelike congruences. We argue that the proposed program can be used in order to express the Sachs optical equations in a covariant form and analyze the confrontation of a spatially inhomogeneous irrotational overdense fluid model with the observational data.
Covariance evaluation work at LANL
Energy Technology Data Exchange (ETDEWEB)
Kawano, Toshihiko [Los Alamos National Laboratory; Talou, Patrick [Los Alamos National Laboratory; Young, Phillip [Los Alamos National Laboratory; Hale, Gerald [Los Alamos National Laboratory; Chadwick, M B [Los Alamos National Laboratory; Little, R C [Los Alamos National Laboratory
2008-01-01
Los Alamos evaluates covariances for nuclear data library, mainly for actinides above the resonance regions and light elements in the enUre energy range. We also develop techniques to evaluate the covariance data, like Bayesian and least-squares fitting methods, which are important to explore the uncertainty information on different types of physical quantities such as elastic scattering angular distribution, or prompt neutron fission spectra. This paper summarizes our current activities of the covariance evaluation work at LANL, including the actinide and light element data mainly for the criticality safety study and transmutation technology. The Bayesian method based on the Kalman filter technique, which combines uncertainties in the theoretical model and experimental data, is discussed.
Lorentz Covariant Canonical Symplectic Algorithms for Dynamics of Charged Particles
Wang, Yulei; Qin, Hong
2016-01-01
In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSA) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of discrete symplectic structure and Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which is difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when th...
Energy Technology Data Exchange (ETDEWEB)
De Felice, Antonio, E-mail: antoniod@nu.ac.th [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); TPTP and NEP, The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400 (Thailand); Kobayashi, Tsutomu [Hakubi Center, Kyoto University, Kyoto 606-8302 (Japan); Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2011-12-06
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G{sub eff} associated with the growth rate of matter perturbations as well as the effective gravitational potential {Phi}{sub eff} relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
De Felice, Antonio; Tsujikawa, Shinji
2011-01-01
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
Virial Theorem for Nonrelativistic Quantum Fields in D Spatial Dimensions
Directory of Open Access Journals (Sweden)
Chris L. Lin
2015-01-01
appearance of a Jacobian J due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the J=1 case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, J=1, is not natural, and the generalization to the case J≠1 is briefly presented.
Covariant description of isothermic surfaces
Tafel, Jacek
2014-01-01
We present a covariant formulation of the Gauss-Weingarten equations and the Gauss-Mainardi-Codazzi equations for surfaces in 3-dimensional curved spaces. We derive a coordinate invariant condition on the first and second fundamental form which is necessary and sufficient for the surface to be isothermic.
Condition Number Regularized Covariance Estimation.
Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala
2013-06-01
Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the "large p small n" setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required.
Condition Number Regularized Covariance Estimation*
Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala
2012-01-01
Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the “large p small n” setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required. PMID:23730197
Covariation Neglect among Novice Investors
Hedesstrom, Ted Martin; Svedsater, Henrik; Garling, Tommy
2006-01-01
In 4 experiments, undergraduates made hypothetical investment choices. In Experiment 1, participants paid more attention to the volatility of individual assets than to the volatility of aggregated portfolios. The results of Experiment 2 show that most participants diversified even when this increased risk because of covariation between the returns…
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Lazarian, A; Takamoto, M; Pino, E M de Gouveia Dal; Cho, J
2015-01-01
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, includi...
From Clifford Algebra of Nonrelativistic Phase Space to Quarks and Leptons of the Standard Model
Żenczykowski, Piotr
2015-01-01
We review a recently proposed Clifford-algebra approach to elementary particles. We start with: (1) a philosophical background that motivates a maximally symmetric treatment of position and momentum variables, and: (2) an analysis of the minimal conceptual assumptions needed in quark mass extraction procedures. With these points in mind, a variation on Born's reciprocity argument provides us with an unorthodox view on the problem of mass. The idea of space quantization suggests then the linearization of the nonrelativistic quadratic form ${\\bf p}^2 +{\\bf x}^2$ with position and momentum satisfying standard commutation relations. This leads to the 64-dimensional Clifford algebra ${Cl}_{6,0}$ of nonrelativistic phase space within which one identifies the internal quantum numbers of a single Standard Model generation of elementary particles (i.e. weak isospin, hypercharge, and color). The relevant quantum numbers are naturally linked to the symmetries of macroscopic phase space. It is shown that the obtained pha...
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Kanazawa, Takuya; Yamamoto, Arata
2016-01-01
We apply QCD-inspired techniques to study nonrelativistic N -component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breaking U (1 )×SU (N )→Sp (N ) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in the ɛ regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.
Dark matter directional detection in non-relativistic effective theories
Catena, Riccardo
2015-01-01
We extend the formalism of dark matter directional detection to arbitrary one-body dark matter-nucleon interactions. The new theoretical framework generalizes the one currently used, which is based on 2 types of dark matter-nucleon interaction only. It includes 14 dark matter-nucleon interaction operators, 8 isotope-dependent nuclear response functions, and the Radon transform of the first 2 moments of the dark matter velocity distribution. We calculate the recoil energy spectra at dark matter directional detectors made of CF$_4$, CS$_2$ and $^{3}$He for the 14 dark matter-nucleon interactions, using nuclear response functions recently obtained through numerical nuclear structure calculations. We highlight the new features of the proposed theoretical framework, and present our results for a spherical dark matter halo and for a stream of dark matter particles. This study lays the foundations for model independent analyses of dark matter directional detection experiments.
Covariant Formulations of Superstring Theories.
Mikovic, Aleksandar Radomir
1990-01-01
Chapter 1 contains a brief introduction to the subject of string theory, and tries to motivate the study of superstrings and covariant formulations. Chapter 2 describes the Green-Schwarz formulation of the superstrings. The Hamiltonian and BRST structure of the theory is analysed in the case of the superparticle. Implications for the superstring case are discussed. Chapter 3 describes the Siegel's formulation of the superstring, which contains only the first class constraints. It is shown that the physical spectrum coincides with that of the Green-Schwarz formulation. In chapter 4 we analyse the BRST structure of the Siegel's formulation. We show that the BRST charge has the wrong cohomology, and propose a modification, called first ilk, which gives the right cohomology. We also propose another superparticle model, called second ilk, which has infinitely many coordinates and constraints. We construct the complete BRST charge for it, and show that it gives the correct cohomology. In chapter 5 we analyse the properties of the covariant vertex operators and the corresponding S-matrix elements by using the Siegel's formulation. We conclude that the knowledge of the ghosts is necessary, even at the tree level, in order to obtain the correct S-matrix. In chapter 6 we attempt to calculate the superstring loops, in a covariant gauge. We calculate the vacuum-to -vacuum amplitude, which is also the cosmological constant. We show that it vanishes to all loop orders, under the assumption that the free covariant gauge-fixed action exists. In chapter 7 we present our conclusions, and briefly discuss the random lattice approach to the string theory, as a possible way of resolving the problem of the covariant quantization and the nonperturbative definition of the superstrings.
A numerical spectral approach for the derivation of piezometric head covariance functions
van Lent, Thomas; Kitanidis, Peter K.
1989-11-01
Relating the variability of permeability to the variability of head is a central part of linear estimation techniques such as cokriging. Only a few analytic relationships between log permeability covariances and head covariances presently exist. This paper describes a general numerical procedure which computes head covariances (ordinary or generalized) and cross covariances for any proper log permeability covariance. The numerical spectral method, a discrete analog of Fourier-Stieltjes analysis, employs the pertinent linearized (small-perturbation approximation) equations describing the physics of flow. The domain is taken as finite, with boundary effects considered negligible. The numerical spectral method can reproduce all pertinent analytic results with excellent agreement. Furthermore, we demonstrate the method's generality by finding the covariance relations for a case where no analytical results presently exist.
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
Németh, Z A
1997-01-01
The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of Lévy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a consistent possibility of coupling them also by axial or chiral type currents. Static self dual vortex solutions together with a vortex-lattice are found with the new couplings.
Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED
Amour, L
2010-01-01
We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. For a fixed total momentum sufficiently small, we study the multiplicity of the ground state of the reduced Hamiltonian. We prove that the coupling between the spins of the charged particles and the electromagnetic field splits the degeneracy of the ground state.
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
Amour, Laurent
2011-01-01
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.
Energy shift of interacting non-relativistic fermions in noncommutative space
Directory of Open Access Journals (Sweden)
A. Jahan
2005-06-01
Full Text Available A local interaction in noncommutative space modifies to a non-local one. For an assembly of particles interacting through the contact potential, formalism of the quantum field theory makes it possible to take into account the effect of modification of the potential on the energy of the system. In this paper we calculate the energy shift of an assembly of non-relativistic fermions, interacting through the contact potential in the presence of the two-dimensional noncommutativity.
Condensation for non-relativistic matter in Hořava–Lifshitz gravity
Directory of Open Access Journals (Sweden)
Jiliang Jing
2015-10-01
Full Text Available We study condensation for non-relativistic matter in a Hořava–Lifshitz black hole without the condition of the detailed balance. We show that, for the fixed non-relativistic parameter α2 (or the detailed balance parameter ϵ, it is easier for the scalar hair to form as the parameter ϵ (or α2 becomes larger, but the condensation is not affected by the non-relativistic parameter β2. We also find that the ratio of the gap frequency in conductivity to the critical temperature decreases with the increase of ϵ and α2, but increases with the increase of β2. The ratio can reduce to the Horowitz–Roberts relation ωg/Tc≈8 obtained in the Einstein gravity and Cai's result ωg/Tc≈13 found in a Hořava–Lifshitz gravity with the condition of the detailed balance for the relativistic matter. Especially, we note that the ratio can arrive at the value of the BCS theory ωg/Tc≈3.5 by taking proper values of the parameters.
Energy Technology Data Exchange (ETDEWEB)
Hussain, S.; Mahmood, S.; Rehman, Aman-ur- [Theoretical Physics Division (TPD), PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Nilore, Islamabad 44000 (Pakistan)
2014-11-15
Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.
Bayesian adjustment for covariate measurement errors: a flexible parametric approach.
Hossain, Shahadut; Gustafson, Paul
2009-05-15
In most epidemiological investigations, the study units are people, the outcome variable (or the response) is a health-related event, and the explanatory variables are usually environmental and/or socio-demographic factors. The fundamental task in such investigations is to quantify the association between the explanatory variables (covariates/exposures) and the outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely the relevant covariates are measured. In many instances, we cannot measure some of the covariates accurately. Rather, we can measure noisy (mismeasured) versions of them. In statistical terminology, mismeasurement in continuous covariates is known as measurement errors or errors-in-variables. Regression analyses based on mismeasured covariates lead to biased inference about the true underlying response-covariate associations. In this paper, we suggest a flexible parametric approach for avoiding this bias when estimating the response-covariate relationship through a logistic regression model. More specifically, we consider the flexible generalized skew-normal and the flexible generalized skew-t distributions for modeling the unobserved true exposure. For inference and computational purposes, we use Bayesian Markov chain Monte Carlo techniques. We investigate the performance of the proposed flexible parametric approach in comparison with a common flexible parametric approach through extensive simulation studies. We also compare the proposed method with the competing flexible parametric method on a real-life data set. Though emphasis is put on the logistic regression model, the proposed method is unified and is applicable to the other generalized linear models, and to other types of non-linear regression models as well. (c) 2009 John Wiley & Sons, Ltd.
Some Algorithms for the Conditional Mean Vector and Covariance Matrix
Directory of Open Access Journals (Sweden)
John F. Monahan
2006-08-01
Full Text Available We consider here the problem of computing the mean vector and covariance matrix for a conditional normal distribution, considering especially a sequence of problems where the conditioning variables are changing. The sweep operator provides one simple general approach that is easy to implement and update. A second, more goal-oriented general method avoids explicit computation of the vector and matrix, while enabling easy evaluation of the conditional density for likelihood computation or easy generation from the conditional distribution. The covariance structure that arises from the special case of an ARMA(p, q time series can be exploited for substantial improvements in computational efficiency.
Covariant Description of Transformation Optics in Linear and Nonlinear Media
Paul, Oliver
2011-01-01
The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstrated for the calculation of the second harmonic generation in a twisted TO concentrator.
On Variance and Covariance for Bounded Linear Operators
Institute of Scientific and Technical Information of China (English)
Chia Shiang LIN
2001-01-01
In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the CauchySchwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type incqualities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities,from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponornal-type operator. Finally, some new characterizations of the Furuta inequality are given.
Stochastic precipitation generator with hidden state covariates
Kim, Yongku; Lee, GyuWon
2017-08-01
Time series of daily weather such as precipitation, minimum temperature and maximum temperature are commonly required for various fields. Stochastic weather generators constitute one of the techniques to produce synthetic daily weather. The recently introduced approach for stochastic weather generators is based on generalized linear modeling (GLM) with covariates to account for seasonality and teleconnections (e.g., with the El Niño). In general, stochastic weather generators tend to underestimate the observed interannual variance of seasonally aggregated variables. To reduce this overdispersion, we incorporated time series of seasonal dry/wet indicators in the GLM weather generator as covariates. These seasonal time series were local (or global) decodings obtained by a hidden Markov model of seasonal total precipitation and implemented in the weather generator. The proposed method is applied to time series of daily weather from Seoul, Korea and Pergamino, Argentina. This method provides a straightforward translation of the uncertainty of the seasonal forecast to the corresponding conditional daily weather statistics.
Energy Technology Data Exchange (ETDEWEB)
Sahu, Biswajit, E-mail: biswajit-sahu@yahoo.co.in [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India); Sinha, Anjana, E-mail: sinha.anjana@gmail.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Department of Mathematics, Visva-Bharati, Santiniketan - 731 204, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700 075 (India)
2015-09-15
A numerical study is presented of the nonlinear dynamics of a magnetized, cold, non-relativistic plasma, in the presence of electron-ion collisions. The ions are considered to be immobile while the electrons move with non-relativistic velocities. The primary interest is to study the effects of the collision parameter, external magnetic field strength, and the initial electromagnetic polarization on the evolution of the plasma system.
[Clinical research XIX. From clinical judgment to analysis of covariance].
Pérez-Rodríguez, Marcela; Palacios-Cruz, Lino; Moreno, Jorge; Rivas-Ruiz, Rodolfo; Talavera, Juan O
2014-01-01
The analysis of covariance (ANCOVA) is based on the general linear models. This technique involves a regression model, often multiple, in which the outcome is presented as a continuous variable, the independent variables are qualitative or are introduced into the model as dummy or dichotomous variables, and factors for which adjustment is required (covariates) can be in any measurement level (i.e. nominal, ordinal or continuous). The maneuvers can be entered into the model as 1) fixed effects, or 2) random effects. The difference between fixed effects and random effects depends on the type of information we want from the analysis of the effects. ANCOVA effect separates the independent variables from the effect of co-variables, i.e., corrects the dependent variable eliminating the influence of covariates, given that these variables change in conjunction with maneuvers or treatments, affecting the outcome variable. ANCOVA should be done only if it meets three assumptions: 1) the relationship between the covariate and the outcome is linear, 2) there is homogeneity of slopes, and 3) the covariate and the independent variable are independent from each other.
The Performance Analysis Based on SAR Sample Covariance Matrix
Directory of Open Access Journals (Sweden)
Esra Erten
2012-03-01
Full Text Available Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.
The covariance of GPS coordinates and frames
Lachièze-Rey, M
2006-01-01
We explore, in the general relativistic context, the properties of the recently introduced GPS coordinates, as well as those of the associated frames and coframes. We show that they are covariant, and completely independent of any observer. We show that standard spectroscopic and astrometric observations allow any observer to measure (i) the values of the GPS coordinates at his position, (ii) the components of his [four-]velocity and (iii) the components of the metric in the GPS frame. This provides to this system an unique value both for conceptual discussion (no frame dependence) and for practical use (involved quantities are directly measurable): localisation, motion monitoring, astrometry, cosmography, tests of gravitation theories. We show explicitly, in the general relativistic context, how an observer may estimate its position and motion, and reconstruct the components of the metric. This arises from two main results: the extension of the velocity fields of the probes to the whole (curved) spacetime; a...
Discrete Symmetries in Covariant LQG
Rovelli, Carlo
2012-01-01
We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spinfoam to occur only across degenerate regions, thus reducing the sources of potential divergences.
Sparse reduced-rank regression with covariance estimation
Chen, Lisha
2014-12-08
Improving the predicting performance of the multiple response regression compared with separate linear regressions is a challenging question. On the one hand, it is desirable to seek model parsimony when facing a large number of parameters. On the other hand, for certain applications it is necessary to take into account the general covariance structure for the errors of the regression model. We assume a reduced-rank regression model and work with the likelihood function with general error covariance to achieve both objectives. In addition we propose to select relevant variables for reduced-rank regression by using a sparsity-inducing penalty, and to estimate the error covariance matrix simultaneously by using a similar penalty on the precision matrix. We develop a numerical algorithm to solve the penalized regression problem. In a simulation study and real data analysis, the new method is compared with two recent methods for multivariate regression and exhibits competitive performance in prediction and variable selection.
Strong decays of excited 1D charmed(-strange) mesons in the covariant oscillator quark model
Maeda, Tomohito; Yoshida, Kento; Yamada, Kenji; Ishida, Shin; Oda, Masuho
2016-05-01
Recently observed charmed mesons, D1* (2760), D3* (2760) and charmed-strange mesons, Ds1 * (2860), Ds3 * (2860), by BaBar and LHCb collaborations are considered to be plausible candidates for c q ¯ 13 DJ (q = u, d, s) states. We calculate the strong decays with one pion (kaon) emission of these states including well-established 1S and 1P charmed(-strange) mesons within the framework of the covariant oscillator quark model. The results obtained are compared with the experimental data and the typical nonrelativistic quark-model calculations. Concerning the results for 1S and 1P states, we find that, thanks to the relativistic effects of decay form factors, our model parameters take reasonable values, though our relativistic approach and the nonrelativistic quark model give similar decay widths in agreement with experiment. While the results obtained for 13 DJ=1,3 states are roughly consistent with the present data, they should be checked by the future precise measurement.
Phenotypic covariance at species’ borders
2013-01-01
Background Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species’ borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes. Results Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species. Conclusions Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species’ borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future. PMID:23714580
Turkington, M. D.; Ballance, C. P.; Hibbert, A.; Ramsbottom, C. A.
2016-08-01
In this work we explore the validity of employing a modified version of the nonrelativistic structure code civ3 for heavy, highly charged systems, using Na-like tungsten as a simple benchmark. Consequently, we present radiative and subsequent collisional atomic data compared with corresponding results from a fully relativistic structure and collisional model. Our motivation for this line of study is to benchmark civ3 against the relativistic grasp0 structure code. This is an important study as civ3 wave functions in nonrelativistic R -matrix calculations are computationally less expensive than their Dirac counterparts. There are very few existing data for the W LXIV ion in the literature with which we can compare except for an incomplete set of energy levels available from the NIST database. The overall accuracy of the present results is thus determined by the comparison between the civ3 and grasp0 structure codes alongside collisional atomic data computed by the R -matrix Breit-Pauli and Dirac codes. It is found that the electron-impact collision strengths and effective collision strengths computed by these differing methods are in good general agreement for the majority of the transitions considered, across a broad range of electron temperatures.
Clarifying the covariant formalism for the SZ effect due to relativistic non-thermal electrons
Boehm, Celine
2008-01-01
We derive the covariant formalism associated with the relativistic Sunyaev-Zel'dovich effect due to a non-thermal population of high energy electrons in clusters of galaxies. More precisely, we show that the formalism proposed by Wright in 1979, based on an empirical approach (but widely used in the literature) to compute the inverse Compton scattering of a population of relativistic electrons on CMB photons, can actually be re-interpreted as a Boltzmann-like equation, in the single scattering approximation. Although this would tend to reconcile Wright's approach with the latest works on the relativistic corrections of the thermal SZ effect, we find that the squared matrix amplitude derived by Wright by applying a relativistic Lorentz boost on Chandrasekhar's non-relativistic formula is incorrect (it is not equivalent to the well-known Compton scattering squared matrix amplitude in the limit of relativistic incoming electrons and low energy photons). This has important consequences. In particular, this modifi...
Alam, Md. Ashad; Fukumizu, Kenji; Wang, Yu-Ping
2016-01-01
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, even when using bounded positive definite kernels. First, we propose robust kernel covariance operator (robust kernel CO) and robust kernel crosscovariance operator (robust kern...
Competing risks and time-dependent covariates
DEFF Research Database (Denmark)
Cortese, Giuliana; Andersen, Per K
2010-01-01
Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates...
Agilan, V.; Umamahesh, N. V.
2017-03-01
Present infrastructure design is primarily based on rainfall Intensity-Duration-Frequency (IDF) curves with so-called stationary assumption. However, in recent years, the extreme precipitation events are increasing due to global climate change and creating non-stationarity in the series. Based on recent theoretical developments in the Extreme Value Theory (EVT), recent studies proposed a methodology for developing non-stationary rainfall IDF curve by incorporating trend in the parameters of the Generalized Extreme Value (GEV) distribution using Time covariate. But, the covariate Time may not be the best covariate and it is important to analyze all possible covariates and find the best covariate to model non-stationarity. In this study, five physical processes, namely, urbanization, local temperature changes, global warming, El Niño-Southern Oscillation (ENSO) cycle and Indian Ocean Dipole (IOD) are used as covariates. Based on these five covariates and their possible combinations, sixty-two non-stationary GEV models are constructed. In addition, two non-stationary GEV models based on Time covariate and one stationary GEV model are also constructed. The best model for each duration rainfall series is chosen based on the corrected Akaike Information Criterion (AICc). From the findings of this study, it is observed that the local processes (i.e., Urbanization, local temperature changes) are the best covariate for short duration rainfall and global processes (i.e., Global warming, ENSO cycle and IOD) are the best covariate for the long duration rainfall of the Hyderabad city, India. Furthermore, the covariate Time is never qualified as the best covariate. In addition, the identified best covariates are further used to develop non-stationary rainfall IDF curves of the Hyderabad city. The proposed methodology can be applied to other situations to develop the non-stationary IDF curves based on the best covariate.
Energy Technology Data Exchange (ETDEWEB)
Bryan, M.F.; Piepel, G.F.; Simpson, D.B.
1996-03-01
The high-level waste (HLW) vitrification plant at the Hanford Site was being designed to transuranic and high-level radioactive waste in borosilicate class. Each batch of plant feed material must meet certain requirements related to plant performance, and the resulting class must meet requirements imposed by the Waste Acceptance Product Specifications. Properties of a process batch and the resultlng glass are largely determined by the composition of the feed material. Empirical models are being developed to estimate some property values from data on feed composition. Methods for checking and documenting compliance with feed and glass requirements must account for various types of uncertainties. This document focuses on the estimation. manipulation, and consequences of composition uncertainty, i.e., the uncertainty inherent in estimates of feed or glass composition. Three components of composition uncertainty will play a role in estimating and checking feed and glass properties: batch-to-batch variability, within-batch uncertainty, and analytical uncertainty. In this document, composition uncertainty and its components are treated in terms of variances and variance components or univariate situations, covariance matrices and covariance components for multivariate situations. The importance of variance and covariance components stems from their crucial role in properly estimating uncertainty In values calculated from a set of observations on a process batch. Two general types of methods for estimating uncertainty are discussed: (1) methods based on data, and (2) methods based on knowledge, assumptions, and opinions about the vitrification process. Data-based methods for estimating variances and covariance matrices are well known. Several types of data-based methods exist for estimation of variance components; those based on the statistical method analysis of variance are discussed, as are the strengths and weaknesses of this approach.
Negative refraction and positive refraction are not Lorentz covariant
Energy Technology Data Exchange (ETDEWEB)
Mackay, Tom G., E-mail: T.Mackay@ed.ac.u [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom)] [NanoMM - Nanoengineered Metamaterials Group, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802-6812 (United States); Lakhtakia, Akhlesh, E-mail: akhlesh@psu.ed [NanoMM - Nanoengineered Metamaterials Group, Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802-6812 (United States)
2009-12-28
Refraction into a half-space occupied by a pseudochiral omega material moving at constant velocity was studied by directly implementing the Lorentz transformations of electric and magnetic fields. Numerical studies revealed that negative refraction, negative phase velocity and counterposition are not Lorentz-covariant phenomenons in general.
Covariance Evaluation Methodology for Neutron Cross Sections
Energy Technology Data Exchange (ETDEWEB)
Herman,M.; Arcilla, R.; Mattoon, C.M.; Mughabghab, S.F.; Oblozinsky, P.; Pigni, M.; Pritychenko, b.; Songzoni, A.A.
2008-09-01
We present the NNDC-BNL methodology for estimating neutron cross section covariances in thermal, resolved resonance, unresolved resonance and fast neutron regions. The three key elements of the methodology are Atlas of Neutron Resonances, nuclear reaction code EMPIRE, and the Bayesian code implementing Kalman filter concept. The covariance data processing, visualization and distribution capabilities are integral components of the NNDC methodology. We illustrate its application on examples including relatively detailed evaluation of covariances for two individual nuclei and massive production of simple covariance estimates for 307 materials. Certain peculiarities regarding evaluation of covariances for resolved resonances and the consistency between resonance parameter uncertainties and thermal cross section uncertainties are also discussed.
Search for non-relativistic magnetic monopoles with IceCube
Energy Technology Data Exchange (ETDEWEB)
Aartsen, M.G.; Hill, G.C.; Robertson, S.; Whelan, B.J. [University of Adelaide, School of Chemistry and Physics, Adelaide, SA (Australia); Abbasi, R.; Ahlers, M.; Arguelles, C.; Baker, M.; BenZvi, S.; Chirkin, D.; Day, M.; Desiati, P.; Diaz-Velez, J.C.; Eisch, J.; Fadiran, O.; Feintzeig, J.; Gladstone, L.; Halzen, F.; Hoshina, K.; Jacobsen, J.; Jero, K.; Karle, A.; Kauer, M.; Kelley, J.L.; Kopper, C.; Krasberg, M.; Kurahashi, N.; Landsman, H.; Maruyama, R.; McNally, F.; Merck, M.; Morse, R.; Riedel, B.; Rodrigues, J.P.; Santander, M.; Tobin, M.N.; Toscano, S.; Van Santen, J.; Weaver, C.; Wellons, M.; Wendt, C.; Westerhoff, S.; Whitehorn, N. [University of Wisconsin, Department of Physics and Wisconsin IceCube Particle Astrophysics Center, Madison, WI (United States); Ackermann, M.; Benabderrahmane, M.L.; Berghaus, P.; Bernardini, E.; Bretz, H.P.; Cruz Silva, A.H.; Gluesenkamp, T.; Jacobi, E.; Kaminsky, B.; Karg, T.; Middell, E.; Mohrmann, L.; Nahnhauer, R.; Schoenwald, A.; Shanidze, R.; Spiering, C.; Stoessl, A.; Yanez, J.P. [DESY, Zeuthen (Germany); Adams, J.; Brown, A.M.; Hickford, S.; Macias, O. [University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch (New Zealand); Aguilar, J.A.; Christov, A.; Montaruli, T.; Rameez, M.; Vallecorsa, S. [Universite de Geneve, Departement de physique nucleaire et corpusculaire, Geneva (Switzerland); Altmann, D.; Classen, L.; Gora, D.; Kappes, A.; Tselengidou, M. [Friedrich-Alexander-Universitaet Erlangen-Nuernberg, Erlangen Centre for Astroparticle Physics, Erlangen (Germany); Arlen, T.C.; De Andre, J.P.A.M.; DeYoung, T.; Dunkman, M.; Eagan, R.; Groh, J.C.; Huang, F.; Quinnan, M.; Smith, M.W.E.; Stanisha, N.A.; Tesic, G. [Pennsylvania State University, Department of Physics, University Park, PA (United States); Auffenberg, J.; Bissok, M.; Blumenthal, J.; Gretskov, P.; Haack, C.; Hallen, P.; Heinen, D.; Jagielski, K.; Kriesten, A.; Krings, K.; Leuermann, M.; Paul, L.; Raedel, L.; Reimann, R.; Schoenen, S.; Schukraft, A.; Vehring, M.; Wallraff, M.; Wiebusch, C.H.; Zierke, S. [RWTH Aachen University, III. Physikalisches Institut, Aachen (Germany); Bai, X.; Evenson, P.A.; Gaisser, T.K.; Gonzalez, J.G.; Hussain, S.; Kuwabara, T.; Ruzybayev, B.; Seckel, D.; Stanev, T.; Tamburro, A.; Tilav, S. [University of Delaware, Bartol Research Institute and Department of Physics and Astronomy, Newark, DE (United States); Barwick, S.W.; Yodh, G. [University of California, Department of Physics and Astronomy, Irvine, CA (United States); Baum, V.; Eberhardt, B.; Koepke, L.; Kroll, G.; Luenemann, J.; Sander, H.G.; Schatto, K.; Wiebe, K. [University of Mainz, Institute of Physics, Mainz (Germany); Bay, R.; Filimonov, K.; Price, P.B.; Woschnagg, K. [University of California, Department of Physics, Berkeley, CA (United States); Beatty, J.J. [Ohio State University, Department of Physics and Center for Cosmology and Astro-Particle Physics, Columbus, OH (United States); Ohio State University, Department of Astronomy, Columbus, OH (United States); Becker Tjus, J.; Eichmann, B.; Fedynitch, A.; Saba, S.M.; Schoeneberg, S.; Unger, E. [Ruhr-Universitaet Bochum, Fakultaet fuer Physik and Astronomie, Bochum (Germany); Becker, K.H.; Bindig, D.; Fischer-Wasels, T.; Helbing, K.; Hoffmann, R.; Klaes, J.; Kopper, S.; Naumann, U.; Obertacke, A.; Omairat, A.; Posselt, J.; Soldin, D.; Tepe, A. [University of Wuppertal, Department of Physics, Wuppertal (Germany); Berley, D.; Blaufuss, E.; Christy, B.; Goodman, J.A.; Hellauer, R.; Hoffman, K.D.; Huelsnitz, W.; Meagher, K.; Olivas, A.; Redl, P.; Richman, M.; Schmidt, T.; Sullivan, G.W.; Wissing, H. [University of Maryland, Department of Physics, College Park, MD (United States); Bernhard, A.; Coenders, S.; Gross, A.; Leute, J.; Resconi, E.; Schulz, O.; Sestayo, Y. [T.U. Munich, Garching (Germany); Besson, D.Z. [University of Kansas, Department of Physics and Astronomy, Lawrence, KS (United States); Binder, G.; Gerhardt, L.; Ha, C.; Klein, S.R.; Miarecki, S. [University of California, Department of Physics, Berkeley, CA (United States); Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Boersma, D.J.; Botner, O.; Euler, S.; Hallgren, A.; Perez de los Heros, C.; Stroem, R.; Taavola, H. [Uppsala University, Department of Physics and Astronomy, Box 516, Uppsala (Sweden); Bohm, C.; Danninger, M.; Finley, C.; Flis, S.; Hulth, P.O.; Hultqvist, K.; Walck, C.; Wolf, M.; Zoll, M. [Stockholm University, Oskar Klein Centre and Department of Physics, Stockholm (Sweden); Bose, D.; Rott, C. [Sungkyunkwan University, Department of Physics, Suwon (Korea, Republic of); Collaboration: IceCube Collaboration; and others
2014-07-15
The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting 1 km{sup 3} of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the Grand Unified Theory (GUT) era shortly after the Big Bang. Depending on the underlying gauge group these monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of 10{sup -27} to 10{sup -21} cm{sup 2}. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of 10{sup -22} (10{sup -24}) cm{sup 2} the flux of non-relativistic GUT monopoles is constrained up to a level of Φ{sub 90} ≤ 10{sup -18} (10{sup -17}) cm{sup -2} s{sup -1} sr{sup -1} at a 90 % confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections. (orig.)
Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
Golkar, Siavash
2014-01-01
We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family tree of primaries with zero particle number and discuss the presence of conservation laws in this sector.
$\\eta_c$ production at the LHC challenges nonrelativistic-QCD factorization
Butenschoen, Mathias; Kniehl, Bernd A
2014-01-01
We analyze the first measurement of $\\eta_c$ production, performed by the LHCb Collaboration, in the nonrelativistic-QCD (NRQCD) factorization framework at next-to-leading order (NLO) in the strong-coupling constant $\\alpha_s$ and the relative velocity $v$ of the bound quarks including the feeddown from $h_c$ mesons. Converting the long-distance matrix elements (LDMEs) extracted by various groups from $J/\\psi$ yield and polarization data to the $\\eta_c$ case using heavy-quark spin symmetry, we find that the resulting NLO NRQCD predictions greatly overshoot the LHCb data, while the color-singlet model provides an excellent description.
Testing the Higgs sector directly in the non-relativistic domain
Zhang, Zhentao
2016-01-01
Directly measuring the Higgs self-coupling is of great importance for testing the Brout-Englert-Higgs mechanism in the Standard Model. As a scattering that contains the direct information from the Higgs self-coupling, we investigate the process $\\mu^-\\mu^+\\rightarrow HH$ in the threshold region. We calculate the one-loop corrections to the cross section and consider the non-perturbative contribution from the Higgs self-interactions in the final state. It is found that the scattering in the non-relativistic domain could be an especial process to testing the Higgs sector directly.
Angular momentum in non-relativistic QED and photon contribution to spin of hydrogen atom
Energy Technology Data Exchange (ETDEWEB)
Chen Panying, E-mail: pychen@umd.ed [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Ji Xiangdong [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Institute of Particle Physics and Cosmology, Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 (China); Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China); Xu Yang [Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China); Zhang Yue [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China)
2010-04-26
We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the individual components of the QED angular momentum up to one loop. We illustrate an application of our results by the first calculation of the angular momentum of the ground state hydrogen atom carried in radiative photons, alpha{sub em}{sup 3}/18pi, which might be measurable in future atomic experiments.
A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
Nicolis, Alberto
2012-01-01
We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. These would normally be associated with gapless Goldstone excitations. We find that, in fact, their currents interpolate gapped excitations. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.
Nonrelativistic gauged quantum mechanics: From Kaluza–Klein compactifications to Bargmann structures
Energy Technology Data Exchange (ETDEWEB)
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-08-14
Highlights: • Null compactification techniques are used to derive the nonrelativistic gauged Schrödinger equation. • Compactification of both Klein–Gordon and Maxwell theories are revisited. • Connections with Kaluza–Klein-like Bargmann frameworks are established. - Abstract: The Schrödinger equation for a spinless particle in presence of an external electromagnetic field is derived by means of null compactification of five dimensional massless Klein–Gordon theory and five–dimensional Maxwell electrodynamics. Connections with Kaluza–Klein-like Bargmann frameworks are established.
η(c) production at the LHC challenges nonrelativistic QCD factorization.
Butenschoen, Mathias; He, Zhi-Guo; Kniehl, Bernd A
2015-03-06
We analyze the first measurement of η_{c} production, performed by the LHCb Collaboration, in the nonrelativistic QCD (NRQCD) factorization framework at next-to-leading order (NLO) in the strong-coupling constant α_{s} and the relative velocity v of the bound quarks including the feeddown from h_{c} mesons. Converting the long-distance matrix elements extracted by various groups from J/ψ yield and polarization data to the η_{c} case using heavy-quark spin symmetry, we find that the resulting NLO NRQCD predictions greatly overshoot the LHCb data, while the color-singlet model provides an excellent description.
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
Lopez-Arcos, Cristhiam; Murugan, Jeff; Nastase, Horatiu
2016-05-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in [1], obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an mathcal{N}=2 Super-Schrödinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this (2 + 1)-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits
Directory of Open Access Journals (Sweden)
J. Niederle
2010-01-01
Full Text Available Two Maxwell-Chern-Simons (MCS models in the (1 + 3-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.
Covariant Hyperbolization of Force-free Electrodynamics
Carrasco, Federico
2016-01-01
Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios, which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications is not feasible to keep the system in that submanifold, and so, it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As already shown by Pfeiffer, a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-possednes for the initial value formulation does not follows. Using the generalized symmetric hyperbolic formalism due to Geroch, we introduce here a covariant hyperbolization for the FFE s...
Supergeometry in locally covariant quantum field theory
Hack, Thomas-Paul; Schenkel, Alexander
2015-01-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...
Universal Gravitation as Lorentz-covariant Dynamics
Kauffmann, Steven Kenneth
2014-01-01
Einstein's equivalence principle implies that the acceleration of a particle in a "specified" gravitational field is independent of its mass. While this is certainly true to great accuracy for bodies we observe in the Earth's gravitational field, a hypothetical body of mass comparable to the Earth's would perceptibly cause the Earth to fall toward it, which would feed back into the strength as a function of time of the Earth's gravitational field affecting that body. In short, Einstein's equivalence principle isn't exact, but is an approximation that ignores recoil of the "specified" gravitational field, which sheds light on why general relativity has no clearly delineated native embodiment of conserved four-momentum. Einstein's 1905 relativity of course doesn't have the inexactitudes he unwittingly built into GR, so it is natural to explore a Lorentz-covariant gravitational theory patterned directly on electromagnetism, wherein a system's zero-divergence overall stress-energy, including all gravitational fee...
Femtosecond Studies Of Coulomb Explosion Utilizing Covariance Mapping
Card, D A
2000-01-01
The studies presented herein elucidate details of the Coulomb explosion event initiated through the interaction of molecular clusters with an intense femtosecond laser beam (≥1 PW/cm2). Clusters studied include ammonia, titanium-hydrocarbon, pyridine, and 7-azaindole. Covariance analysis is presented as a general technique to study the dynamical processes in clusters and to discern whether the fragmentation channels are competitive. Positive covariance determinations identify concerted processes such as the concomitant explosion of protonated cluster ions of asymmetrical size. Anti- covariance mapping is exploited to distinguish competitive reaction channels such as the production of highly charged nitrogen atoms formed at the expense of the protonated members of a cluster ion ensemble. This technique is exemplified in each cluster system studied. Kinetic energy analyses, from experiment and simulation, are presented to fully understand the Coulomb explosion event. A cutoff study strongly suggests that...
Data Covariances from R-Matrix Analyses of Light Nuclei
Energy Technology Data Exchange (ETDEWEB)
Hale, G.M., E-mail: ghale@lanl.gov; Paris, M.W.
2015-01-15
After first reviewing the parametric description of light-element reactions in multichannel systems using R-matrix theory and features of the general LANL R-matrix analysis code EDA, we describe how its chi-square minimization procedure gives parameter covariances. This information is used, together with analytically calculated sensitivity derivatives, to obtain cross section covariances for all reactions included in the analysis by first-order error propagation. Examples are given of the covariances obtained for systems with few resonances ({sup 5}He) and with many resonances ({sup 13}C ). We discuss the prevalent problem of this method leading to cross section uncertainty estimates that are unreasonably small for large data sets. The answer to this problem appears to be using parameter confidence intervals in place of standard errors.
Flavour Covariant Transport Equations: an Application to Resonant Leptogenesis
Dev, P S Bhupal; Pilaftsis, Apostolos; Teresi, Daniele
2014-01-01
We present a fully flavour-covariant formalism for transport phenomena, by deriving Markovian master equations that describe the time-evolution of particle number densities in a statistical ensemble with arbitrary flavour content. As an application of this general formalism, we study flavour effects in a scenario of resonant leptogenesis (RL) and obtain the flavour-covariant evolution equations for heavy-neutrino and lepton number densities. This provides a complete and unified description of RL, capturing three relevant physical phenomena: (i) the resonant mixing between the heavy-neutrino states, (ii) coherent oscillations between different heavy-neutrino flavours, and (iii) quantum decoherence effects in the charged-lepton sector. To illustrate the importance of this formalism, we numerically solve the flavour-covariant rate equations for a minimal RL model and show that the total lepton asymmetry can be enhanced up to one order of magnitude, as compared to that obtained from flavour-diagonal or partially ...
Covariate-adjusted confidence interval for the intraclass correlation coefficient.
Shoukri, Mohamed M; Donner, Allan; El-Dali, Abdelmoneim
2013-09-01
A crucial step in designing a new study is to estimate the required sample size. For a design involving cluster sampling, the appropriate sample size depends on the so-called design effect, which is a function of the average cluster size and the intracluster correlation coefficient (ICC). It is well-known that under the framework of hierarchical and generalized linear models, a reduction in residual error may be achieved by including risk factors as covariates. In this paper we show that the covariate design, indicating whether the covariates are measured at the cluster level or at the within-cluster subject level affects the estimation of the ICC, and hence the design effect. Therefore, the distinction between these two types of covariates should be made at the design stage. In this paper we use the nested-bootstrap method to assess the accuracy of the estimated ICC for continuous and binary response variables under different covariate structures. The codes of two SAS macros are made available by the authors for interested readers to facilitate the construction of confidence intervals for the ICC. Moreover, using Monte Carlo simulations we evaluate the relative efficiency of the estimators and evaluate the accuracy of the coverage probabilities of a 95% confidence interval on the population ICC. The methodology is illustrated using a published data set of blood pressure measurements taken on family members.
Covariance and correlation estimation in electron-density maps.
Altomare, Angela; Cuocci, Corrado; Giacovazzo, Carmelo; Moliterni, Anna; Rizzi, Rosanna
2012-03-01
Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution.
On the Estimation of Integrated Covariance Matrices of High Dimensional Diffusion Processes
Zheng, Xinghua
2010-01-01
We consider the estimation of integrated covariance matrices of high dimensional diffusion processes by using high frequency data. We start by studying the most commonly used estimator, the realized covariance matrix (RCV). We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV depends on the covolatility processes not only through the underlying integrated covariance matrix Sigma, but also on how the covolatility processes vary in time. In particular, for two high dimensional diffusion processes with the same integrated covariance matrix, the empirical spectral distributions of their RCVs can be very different. Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in general \\emph{not} a good proxy to rely on in the high dimensional case. We then propose an alternative estimator, the time-variation adjusted realized covariance matrix (TVARCV), for ...
Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
Khoury, Justin; Tolley, Andrew J
2011-01-01
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of general covariance. In this paper, we explore modifications of general relativity that retain the same number of gravitational degrees of freedom, and therefore explicitly break general covariance. Motivated by cosmology, the modifications of interest maintain spatial covariance. Demanding consistency of the theory forces the physical Hamiltonian density to obey an analogue of the renormalization group equation. In this context, the equation encodes the invariance of the theory under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.
Quantum Gravity from the Point of View of Locally Covariant Quantum Field Theory
Brunetti, Romeo; Fredenhagen, Klaus; Rejzner, Katarzyna
2016-08-01
We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.
Hamiltonian approach to GR - Part 1: covariant theory of classical gravity
Cremaschini, Claudio
2016-01-01
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor $\\hat{g}(r)\\equiv \\left\\{ \\hat{g}_{\\mu \
Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates
Lockwood, J. R.; McCaffrey, Daniel F.
2015-01-01
Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with…
Leitão, Sofia; Stadler, Alfred; Peña, M. T.; Biernat, Elmar P.
2017-01-01
The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy-light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The numerical calculations are performed in momentum space, where special care is taken to treat the strong singularities present in the confining kernel. The observed meson spectrum is very well reproduced after fitting a small number of model parameters. Remarkably, a fit to a few pseudoscalar meson states only, which are insensitive to spin-orbit and tensor forces and do not allow to separate the spin-spin from the central interaction, leads to essentially the same model parameters as a more general fit. This demonstrates that the covariance of the chosen interaction kernel is responsible for the very accurate prediction of the spin-dependent quark-antiquark interactions.
Leitão, Sofia; Peña, M T; Biernat, Elmar P
2016-01-01
The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy-light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The numerical calculations are performed in momentum space, where special care is taken to treat the strong singularities present in the confining kernel. The observed meson spectrum is very well reproduced after fitting a small number of model parameters. Remarkably, a fit to a few pseudoscalar meson states only, which are insensitive to spin-orbit and tensor forces and do not allow to separate the spin-spin from the central interaction, leads to essentially the same model parameters as a more general fit. This demonstrates that the covariance of the chosen interaction kernel is responsible for the very accurate prediction of the spin-dependent quark-antiquark interactions.
Velocity operator and velocity field for spinning particles in (non-relativistic) quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Recami, E. [Bergamo Univ. (Italy). Facolta` di Ingegneria]|[INFN, Milan (Italy)]|[Campinas State Univ., SP (Brazil). Dept. of Applied Math.; Salesi, G. [Catania Univ. (Italy). Dip. di Fisica
1995-06-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, the paper introduces - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, a new (non-relativistic) velocity operator for a spin 1/2 particle is also proposed. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of- mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework, i.e. in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which the constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current.
Harada, Koji; Yoshimoto, Issei
2012-01-01
Low-energy effective field theory describing a nonrelativistic three-body system is analyzed in the Wilsonian renormalization group (RG) method. No effective auxiliary field (dimeron) that corresponds to two-body propagation is introduced. The Efimov effect is expected in the case of an infinite two-body scattering length, and is believed to be related to the limit cycle behavior in the three-body renormalization group equations (RGEs). If the one-loop property of the RGEs for the nonrelativistic system without the dimeron field, which is essential in deriving RGEs in the two-body sector, persists in the three-body sector, it appears to prevent the emergence of limit cycle behavior. We explain how the multi-loop diagrams contribute in the three-body sector without contradicting the one-loop property of the RGEs, and derive the correct RGEs, which lead to the limit cycle behavior. The Efimov parameter, $s_{0}$, is obtained within a few percent error in the leading orders. We also remark on the correct use of t...
Search for non-relativistic Magnetic Monopoles with IceCube
Aartsen, M G; Ackermann, M; Adams, J; Aguilar, J A; Ahlers, M; Altmann, D; Arguelles, C; Arlen, T C; Auffenberg, J; Bai, X; Baker, M; Barwick, S W; Baum, V; Bay, R; Beatty, J J; Tjus, J Becker; Becker, K -H; Benabderrahmane, M L; BenZvi, S; Berghaus, P; Berley, D; Bernardini, E; Bernhard, A; Besson, D Z; Binder, G; Bindig, D; Bissok, M; Blaufuss, E; Blumenthal, J; Boersma, D J; Bohm, C; Bose, D; Böser, S; Botner, O; Brayeur, L; Bretz, H -P; Brown, A M; Bruijn, R; Casey, J; Casier, M; Chirkin, D; Christov, A; Christy, B; Clark, K; Classen, L; Clevermann, F; Coenders, S; Cohen, S; Cowen, D F; Silva, A H Cruz; Danninger, M; Daughhetee, J; Davis, J C; Day, M; de André, J P A M; De Clercq, C; De Ridder, S; Desiati, P; de Vries, K D; de With, M; DeYoung, T; Díaz-Vélez, J C; Dunkman, M; Eagan, R; Eberhardt, B; Eichmann, B; Eisch, J; Euler, S; Evenson, P A; Fadiran, O; Fazely, A R; Fedynitch, A; Feintzeig, J; Feusels, T; Filimonov, K; Finley, C; Fischer-Wasels, T; Flis, S; Franckowiak, A; Frantzen, K; Fuchs, T; Gaisser, T K; Gallagher, J; Gerhardt, L; Gladstone, L; Glüsenkamp, T; Goldschmidt, A; Golup, G; Gonzalez, J G; Goodman, J A; Góra, D; Grandmont, D T; Grant, D; Gretskov, P; Groh, J C; Groß, A; Ha, C; Haack, C; Ismail, A Haj; Hallen, P; Hallgren, A; Halzen, F; Hanson, K; Hebecker, D; Heereman, D; Heinen, D; Helbing, K; Hellauer, R; Hickford, S; Hill, G C; Hoffman, K D; Hoffmann, R; Homeier, A; Hoshina, K; Huang, F; Huelsnitz, W; Hulth, P O; Hultqvist, K; Hussain, S; Ishihara, A; Jacobi, E; Jacobsen, J; Jagielski, K; Japaridze, G S; Jero, K; Jlelati, O; Kaminsky, B; Kappes, A; Karg, T; Karle, A; Kauer, M; Kelley, J L; Kiryluk, J; Kläs, J; Klein, S R; Köhne, J -H; Kohnen, G; Kolanoski, H; Köpke, L; Kopper, C; Kopper, S; Koskinen, D J; Kowalski, M; Krasberg, M; Kriesten, A; Krings, K; Kroll, G; Kunnen, J; Kurahashi, N; Kuwabara, T; Labare, M; Landsman, H; Larson, M J; Lesiak-Bzdak, M; Leuermann, M; Leute, J; Lünemann, J; Macías, O; Madsen, J; Maggi, G; Maruyama, R; Mase, K; Matis, H S; McNally, F; Meagher, K; Meli, A; Merck, M; Meures, T; Miarecki, S; Middell, E; Milke, N; Miller, J; Mohrmann, L; Montaruli, T; Morse, R; Nahnhauer, R; Naumann, U; Niederhausen, H; Nowicki, S C; Nygren, D R; Obertacke, A; Odrowski, S; Olivas, A; Omairat, A; O'Murchadha, A; Palczewski, T; Paul, L; Pepper, J A; Heros, C Pérez de los; Pfendner, C; Pieloth, D; Pinat, E; Posselt, J; Price, P B; Przybylski, G T; Quinnan, M; Rädel, L; Rameez, M; Rawlins, K; Redl, P; Reimann, R; Resconi, E; Rhode, W; Ribordy, M; Richman, M; Riedel, B; Robertson, S; Rodrigues, J P; Rott, C; Ruhe, T; Ruzybayev, B; Ryckbosch, D; Saba, S M; Sander, H -G; Santander, M; Sarkar, S; Schatto, K; Scheriau, F; Schmidt, T; Schmitz, M; Schoenen, S; Schöneberg, S; Schönwald, A; Schukraft, A; Schulte, L; Schulz, O; Seckel, D; Sestayo, Y; Seunarine, S; Shanidze, R; Sheremata, C; Smith, M W E; Soldin, D; Spiczak, G M; Spiering, C; Stamatikos, M; Stanev, T; Stanisha, N A; Stasik, A; Stezelberger, T; Stokstad, R G; Stößl, A; Strahler, E A; Ström, R; Strotjohann, N L; Sullivan, G W; Taavola, H; Taboada, I; Tamburro, A; Tepe, A; Ter-Antonyan, S; Tešić, G; Tilav, S; Toale, P A; Tobin, M N; Toscano, S; Tselengidou, M; Unger, E; Usner, M; Vallecorsa, S; van Eijndhoven, N; van Santen, J; Vehring, M; Voge, M; Vraeghe, M; Walck, C; Wallraff, M; Weaver, Ch; Wellons, M; Wendt, C; Westerhoff, S; Whelan, B J; Whitehorn, N; Wiebe, K; Wiebusch, C H; Williams, D R; Wissing, H; Wolf, M; Wood, T R; Woschnagg, K; Xu, D L; Xu, X W; Yanez, J P; Yodh, G; Yoshida, S; Zarzhitsky, P; Ziemann, J; Zierke, S; Zoll, M
2014-01-01
The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\\,\\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\\,\\mathrm{cm^2}$ to $10^{-21}\\,\\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal ...
Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks
Caprioli, Damiano; Pop, Ana-Roxana; Spitkovsky, Anatoly
2015-01-01
We use kinetic hybrid simulations (kinetic ions-fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also, by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.
Convex Decompositions of Thermal Equilibrium for Non-interacting Non-relativistic Particles
Chenu, Aurelia; Branczyk, Agata; Sipe, John
2016-05-01
We provide convex decompositions of thermal equilibrium for non-interacting non-relativistic particles in terms of localized wave packets. These quantum representations offer a new tool and provide insights that can help relate to the classical picture. Considering that thermal states are ubiquitous in a wide diversity of fields, studying different convex decompositions of the canonical ensemble is an interesting problem by itself. The usual classical and quantum pictures of thermal equilibrium of N non-interacting, non-relativistic particles in a box of volume V are quite different. The picture in classical statistical mechanics is about (localized) particles with a range of positions and velocities; in quantum statistical mechanics, one considers the particles (bosons or fermions) associated with energy eigenstates that are delocalized through the whole box. Here we provide a representation of thermal equilibrium in quantum statistical mechanics involving wave packets with a localized coordinate representation and an expectation value of velocity. In addition to derive a formalism that may help simplify particular calculations, our results can be expected to provide insights into the transition from quantum to classical features of the fully quantum thermal state.
Generalized Galilean Algebras and Newtonian Gravity
Albornoz, N L González; Salgado, P; Salgado, S
2016-01-01
The non-relativistic versions of the generalized Poincar\\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by $\\mathcal{G}\\mathfrak{B}_{n}$ and $\\mathcal{G}\\mathfrak{L}_{_{n}}$ respectively. Using a generalized In\\"{o}n\\"{u}--Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The $S$-expansion procedure allows us to find the $\\mathcal{G}\\mathfrak{B}_{_{5}}$ algebra from the Newton--Hooke algebra with central extension. The procedure developed in Ref. \\cite{newton} allow us to show that the non-relativistic limit of the five dimensional Einstein--Chern--Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2016-01-01
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
ISSUES IN NEUTRON CROSS SECTION COVARIANCES
Energy Technology Data Exchange (ETDEWEB)
Mattoon, C.M.; Oblozinsky,P.
2010-04-30
We review neutron cross section covariances in both the resonance and fast neutron regions with the goal to identify existing issues in evaluation methods and their impact on covariances. We also outline ideas for suitable covariance quality assurance procedures.We show that the topic of covariance data remains controversial, the evaluation methodologies are not fully established and covariances produced by different approaches have unacceptable spread. The main controversy is in very low uncertainties generated by rigorous evaluation methods and much larger uncertainties based on simple estimates from experimental data. Since the evaluators tend to trust the former, while the users tend to trust the latter, this controversy has considerable practical implications. Dedicated effort is needed to arrive at covariance evaluation methods that would resolve this issue and produce results accepted internationally both by evaluators and users.
Parameter inference with estimated covariance matrices
Sellentin, Elena
2015-01-01
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be estimated and thereby becomes a random object with some intrinsic uncertainty itself. We show how to infer parameters in the presence of such an estimated covariance matrix, by marginalising over the true covariance matrix, conditioned on its estimated value. This leads to a likelihood function that is no longer Gaussian, but rather an adapted version of a multivariate $t$-distribution, which has the same numerical complexity as the multivariate Gaussian. As expected, marginalisation over the true covariance matrix improves inference when compared with Hartlap et al.'s method, which uses an unbiased estimate of the inverse covariance matrix but still assumes that the likelihood is Gaussian.
ISSUES IN NEUTRON CROSS SECTION COVARIANCES
Energy Technology Data Exchange (ETDEWEB)
Mattoon, C.M.; Oblozinsky,P.
2010-04-30
We review neutron cross section covariances in both the resonance and fast neutron regions with the goal to identify existing issues in evaluation methods and their impact on covariances. We also outline ideas for suitable covariance quality assurance procedures.We show that the topic of covariance data remains controversial, the evaluation methodologies are not fully established and covariances produced by different approaches have unacceptable spread. The main controversy is in very low uncertainties generated by rigorous evaluation methods and much larger uncertainties based on simple estimates from experimental data. Since the evaluators tend to trust the former, while the users tend to trust the latter, this controversy has considerable practical implications. Dedicated effort is needed to arrive at covariance evaluation methods that would resolve this issue and produce results accepted internationally both by evaluators and users.
Treatment Effects with Many Covariates and Heteroskedasticity
DEFF Research Database (Denmark)
Cattaneo, Matias D.; Jansson, Michael; Newey, Whitney K.
The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtai......The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results...... then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: (i) parametric linear models with many covariates, (ii...
Covariance matrices for use in criticality safety predictability studies
Energy Technology Data Exchange (ETDEWEB)
Derrien, H.; Larson, N.M.; Leal, L.C.
1997-09-01
Criticality predictability applications require as input the best available information on fissile and other nuclides. In recent years important work has been performed in the analysis of neutron transmission and cross-section data for fissile nuclei in the resonance region by using the computer code SAMMY. The code uses Bayes method (a form of generalized least squares) for sequential analyses of several sets of experimental data. Values for Reich-Moore resonance parameters, their covariances, and the derivatives with respect to the adjusted parameters (data sensitivities) are obtained. In general, the parameter file contains several thousand values and the dimension of the covariance matrices is correspondingly large. These matrices are not reported in the current evaluated data files due to their large dimensions and to the inadequacy of the file formats. The present work has two goals: the first is to calculate the covariances of group-averaged cross sections from the covariance files generated by SAMMY, because these can be more readily utilized in criticality predictability calculations. The second goal is to propose a more practical interface between SAMMY and the evaluated files. Examples are given for {sup 235}U in the popular 199- and 238-group structures, using the latest ORNL evaluation of the {sup 235}U resonance parameters.
Eigenvalue variance bounds for covariance matrices
Dallaporta, Sandrine
2013-01-01
This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for Wigner matrices and stated the results for covariance matrices. They are proved in the present paper. Relying on the LUE example, which needs to be investigated first, the main bounds are extended to complex covariance matrices by means of the Tao, Vu and Wan...
Dielectric laser acceleration of non-relativistic electrons at a photonic structure
Energy Technology Data Exchange (ETDEWEB)
Breuer, John
2013-08-29
This thesis reports on the observation of dielectric laser acceleration of non-relativistic electrons via the inverse Smith-Purcell effect in the optical regime. Evanescent modes in the vicinity of a periodic grating structure can travel at the same velocity as the electrons along the grating surface. A longitudinal electric field component is used to continuously impart momentum onto the electrons. This is only possible in the near-field of a suitable photonic structure, which means that the electron beam has to pass the structure within about one wavelength. In our experiment we exploit the third spatial harmonic of a single fused silica grating excited by laser pulses derived from a Titanium:sapphire oscillator and accelerate non-relativistic 28 keV electrons. We measure a maximum energy gain of 280 eV, corresponding to an acceleration gradient of 25 MeV/m, already comparable with state-of-the-art radio-frequency linear accelerators. To experience this acceleration gradient the electrons approach the grating closer than 100 nm. We present the theory behind grating-based particle acceleration and discuss simulation results of dielectric laser acceleration in the near-field of photonic grating structures, which is excited by near-infrared laser light. Our measurements show excellent agreement with our simulation results and therefore confirm the direct acceleration with the light field. We further discuss the acceleration inside double grating structures, dephasing effects of non-relativistic electrons as well as the space charge effect, which can limit the attainable peak currents of these novel accelerator structures. The photonic structures described in this work can be readily concatenated and therefore represent a scalable realization of dielectric laser acceleration. Furthermore, our structures are directly compatible with the microstructures used for the acceleration of relativistic electrons demonstrated in parallel to this work by our collaborators in
Davies, Christopher E; Glonek, Gary Fv; Giles, Lynne C
2017-08-01
One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost.
Historical Hamiltonian Dynamics: symplectic and covariant
Lachieze-Rey, M
2016-01-01
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field theories on space-time. It is based on the notion of (Hamiltonian) histories, which are sections of the (extended) phase space bundle. It is developed in the space of sections, in contradistinction with the usual formalism which works in the bundle manifold. In field theories, the formalism remains covariant and does not require a spitting of space-time. It considers space-time exactly in the same manner than time in usual dynamics, both being particular cases of the evolution domain. It applies without modification when the histories (the fields) are forms rather than scalar functions, like in electromagnetism or in tetrad general relativity. We develop a differential calculus in the infinite dimensional space of histories. It admits a (generalized) symplectic form which d...
Pan, Guangming; Zhou, Wang
2010-01-01
A consistent kernel estimator of the limiting spectral distribution of general sample covariance matrices was introduced in Jing, Pan, Shao and Zhou (2010). The central limit theorem of the kernel estimator is proved in this paper.
Construction of the ground state in nonrelativistic QED by continuous flows
Bach, Volker; Könenberg, Martin
For a nonrelativistic hydrogen atom minimally coupled to the quantized radiation field we construct the ground state projection P by a continuous approximation scheme as an alternative to the iteration scheme recently used by Fröhlich, Pizzo, and the first author [V. Bach, J. Fröhlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys. (2006), doi: 10.1007/s00220-005-1478-3]. That is, we construct P=limP as the limit of a continuously differentiable family ()t⩾0 of ground state projections of infrared regularized Hamiltonians H. Using the ODE solved by this family of projections, we show that the norm ‖P‖ of their derivative is integrable in t which in turn yields the convergence of P by the fundamental theorem of calculus.
Caprioli, Damiano
2014-01-01
We use large hybrid (kinetic ions-fluid electrons) simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of energetic particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient (at quasi-parallel shocks), we find that the magnetic field develops transverse components and is significantly amplified in the pre-shock medium. The total amplification factor is larger than 10 for shocks with Mach number $M=100$, and scales with the square root of $M$. We find that in the shock precursor the energy spectral density of excited magnetic turbulence is proportional to spectral energy distribution of accelerated particles at corresponding resonant momenta, in good agreement with the predictions of quasilinear theory of diffusive shock acceleration. We discuss the role of Bell's instability, which is predicted and found to grow faster than resonant instability in shocks with $M\\gtrsim 30$. Ahead of these strong shocks we distinguis...
Path integral polymer propagator of relativistic and non-relativistic particles
Morales-Técotl, Hugo A; Ruelas, Juan C
2016-01-01
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer Propagators previously obtained by spectral methods for a nonrelativistic polymer particle, both free and in a box, are regained with this method. Remarkably, the approach is also shown to yield the polymer propagator of the relativistic particle. This reduces to the standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Some possible future developments are commented upon.
Ultra high energy cosmic rays from non-relativistic quasar outflows
Wang, Xiawei
2016-01-01
It has been suggested that non-relativistic outflows from quasars can naturally account for the missing component of the extragalactic $\\gamma$-ray background and explain the cumulative neutrino background through pion decay in collisions between protons accelerated by the outflow shock and interstellar protons. Here we show that the same quasar outflows are capable of accelerating protons to energies of $\\sim 10^{20}$ eV during the early phase of their propagation. The overall quasar population is expected to produce a cumulative ultra high energy cosmic ray flux of $\\sim10^{-7}\\,\\rm GeV\\,cm^{-2}s^{-1}sr^{-1}$ at $E_{\\rm CR}\\gtrsim10^{18}$ eV. The spectral shape and amplitude is consistent with recent observations for outflow parameters constrained to fit secondary $\\gamma$-rays and neutrinos without any additional parameter tuning. This indicates that quasar outflows simultaneously account for all three messengers at their observed levels.
On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field
Amour, Laurent; Grebert, Benoit; Guillot, Jean-Claude
2008-01-01
We consider a non-relativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. The system is translation invariant in the $x_3$-direction and we consider the reduced Hamiltonian $H(P_3)$ associated with the total momentum $P_3$ along the $x_3$-axis. For a fixed momentum $P_3$ sufficiently small, we prove that $H(P_3)$ has a ground state in the Fock representation if and only if $E'(P_3)=0$, where $P_3 \\mapsto E'(P_3)$ is the derivative of the map $P_3 \\mapsto E(P_3) = \\inf \\sigma (H(P_3))$. If $E'(P_3) \
Energy Technology Data Exchange (ETDEWEB)
Butenschoen, Mathias; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2009-09-15
We calculate the cross section of inclusive direct J/{psi} photoproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics, for the first time including the full relativistic corrections due to the intermediate {sup 1}S{sub 0}{sup [8]}, {sup 3}S{sub 1}{sup [8]}, and {sup 3}P{sub J}{sup [8]} color-octet states. A comparison of our results to recent H1 data suggests that the color octet mechanism is indeed realized in J/{psi} photoproduction, although the predictivity of our results still suffers from uncertainties in the color-octet long-distance matrix elements. (orig.)
Failure of relativistic codes in the non-relativistic limit: the role of Brillouin configurations
Indelicato, P J; Desclaux, J P
2004-01-01
In the present letter we solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method. We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We identify the role of single excitations obeying to Brillouin's theorem in this problem. We show that with large scale calculations in which this problem is properly treated, we can reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED
Investigation of Properties of Exotic Nuclei in Non-relativistic and Relativistic Models
Institute of Scientific and Technical Information of China (English)
2001-01-01
Properties of exotic nuclei are described by non-relativistic and relativistic models. The relativistic mean field theory predicts one proton halo in 26,27,28P and two proton halos in 27,28,29S, recently, one proton halo in 26,27,28P has been found experimentally in MSU lab. The relativistic Hartree-Fock theory has been used to investigate the contribution of Fock term and isovector mesons to the properties of exotic nuclei. It turns out that the influence of the Fock term and isovector mesons on the properties of neutron extremely rich nuclei is very different from that of near stable nuclei. Meanwhile, the deformed Hartree-Fock-Bogoliubov theory has been employed to describe the ground state properties of the isotopes for some light nuclei.
Energy modulation of nonrelativistic electrons in an optical near field on a metal microslit
Ishikawa, R.; Bae, J.; Mizuno, K.
2001-04-01
Energy modulation of nonrelativistic electrons with a laser beam using a metal microslit as an interaction circuit has been investigated. An optical near field is induced in the proximity of the microslit by illumination of the laser beam. The electrons passing close to the slit are accelerated or decelerated by an evanescent wave contained in the near field whose phase velocity is equal to the velocity of the electrons. The electron-evanescent wave interaction in the microslit has been analyzed theoretically and experimentally. The theory has predicted that electron energy can be modulated at optical frequencies. Experiments performed in the infrared region have verified theoretical predictions. The electron-energy changes of more than ±5 eV with a 10 kW CO2 laser pulse at the wavelength of 10.6 μm has been successfully observed for an electron beam with an energy of less than 80 keV.
Semi-classical locality for the non-relativistic path integral in configuration space
Gomes, Henrique
2015-01-01
In an accompanying paper, we have put forward an interpretation of quantum mechanics grounded on a non-relativistic Lagrangian 3+1 formalism of a closed Universe, existing on timeless configuration space. However, not much was said there about the role of locality, which was not assumed. In this paper, I describe how subsystems existing in (spatial) regions with fixed boundary conditions can be represented as submanifolds of the complete configuration space. I show that if the action functional can be put in the form of Riemannian distance element, then dynamical independence of the subsystem implies that the respective submanifolds are totally geodesic. When two regions are mutually independent the semi-classical path integral kernel factorizes, showing cluster decomposition. To exemplify these constructions I then construct a specific gravitational system with two propagating physical degrees of freedom and no refoliation-invariance. Finally, considering the path integral in this 3+1 context, I implement an...
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
Lopez-Arcos, Cristhiam; Nastase, Horatiu
2015-01-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in \\cite{Mohammed:2012gi}, obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an ${\\cal N}=2$ Super-Schr\\"odinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this $(2+1)$-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
Static spherically symmetric solutions in the IR limit of nonrelativistic quantum gravity
Harada, Tomohiro; Tsukamoto, Naoki
2009-01-01
We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalisable quantum gravity recently proposed by Ho\\v{r}ava. It is found that the projectability condition plays an important role. Without the cosmological constant, the spacetime is uniquely given by the Schwarzschild solution. With the cosmological constant, the spacetime is uniquely given by the Kottler (Schwarzschild-(anti) de Sitter) solution for the entirely vacuum spacetime. However, the ``ultra-static'' metric of spherical and hyperbolic spaces can be also admissible for the locally empty region, for the positive and negative cosmological constants, respectively, if its nonvanishing contribution to the global Hamiltonian constraint can be compensated by that from the nonempty or nonstatic region. This implies that static spherically symmetric entirely vacuum solutions would not admit the freedom to reproduce the observed flat rotation curves of galaxies. On the...
Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
Wachter, H
2007-01-01
This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation are given. Expressions for their iterative solutions are written down. It is shown how to calculate S-matrices and transition probabilities. Furthermore, attention is focused on the question what becomes of unitarity of S-matrices in a q-deformed setting. The examinations are concluded by a discussion of the interaction picture and its relation to scattering processes.
Electron acceleration in a nonrelativistic shock with very high Alfv\\'en Mach number
Matsumoto, Y; Hoshino, M
2013-01-01
Electron acceleration associated with various plasma kinetic instabilities in a nonrelativistic, very-high-Alfv\\'en Mach-number ($M_A \\sim 45$) shock is revealed by means of a two-dimensional fully kinetic PIC simulation. Electromagnetic (ion Weibel) and electrostatic (ion-acoustic and Buneman) instabilities are strongly activated at the same time in different regions of the two-dimensional shock structure. Relativistic electrons are quickly produced predominantly by the shock surfing mechanism with the Buneman instability at the leading edge of the foot. The energy spectrum has a high-energy tail exceeding the upstream ion kinetic energy accompanying the main thermal population. This gives a favorable condition for the ion acoustic instability at the shock front, which in turn results in additional energization. The large-amplitude ion Weibel instability generates current sheets in the foot, implying another dissipation mechanism via magnetic reconnection in a three-dimensional shock structure in the very-hi...
Covariance structure models of expectancy.
Henderson, M J; Goldman, M S; Coovert, M D; Carnevalla, N
1994-05-01
Antecedent variables under the broad categories of genetic, environmental and cultural influences have been linked to the risk for alcohol abuse. Such risk factors have not been shown to result in high correlations with alcohol consumption and leave unclear an understanding of the mechanism by which these variables lead to increased risk. This study employed covariance structure modeling to examine the mediational influence of stored information in memory about alcohol, alcohol expectancies in relation to two biologically and environmentally driven antecedent variables, family history of alcohol abuse and a sensation-seeking temperament in a college population. We also examined the effect of criterion contamination on the relationship between sensation-seeking and alcohol consumption. Results indicated that alcohol expectancy acts as a significant, partial mediator of the relationship between sensation-seeking and consumption, that family history of alcohol abuse is not related to drinking outcome and that overlap in items on sensation-seeking and alcohol consumption measures may falsely inflate their relationship.
Chavanis, Pierre-Henri
2016-01-01
We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of weak gravitational fields in a static or expanding background, and the nonrelativistic (Newtonian) limit. The Klein-Gordon-Maxwell-Einstein equations govern the evolution of a complex scalar field, possibly describing self-gravitating Bose-Einstein condensates, coupled to an electromagnetic field. They may find applications in the context of dark matter, boson stars, and neutron stars with a superfluid core.
COVARIATION BIAS AND THE RETURN OF FEAR
de Jong, Peter; VANDENHOUT, MA; MERCKELBACH, H
1995-01-01
Several studies have indicated that phobic fear is accompanied by a covariation bias, i.e. that phobic Ss tend to overassociate fear relevant stimuli and aversive outcomes. Such a covariation bias seems to be a fairly direct and powerful way to confirm danger expectations and enhance fear. Therefore
Covariant derivative of fermions and all that
Shapiro, Ilya L
2016-01-01
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. The text represents a part of the initial chapter of a one-semester course on semiclassical gravity.
De Soto, F
2006-01-01
The numerical solutions of the non-relativistic Yukawa model on a 3-dimensional size lattice with periodic boundary conditions are obtained. The possibility to extract the corresponding -- infinite space -- low energy parameters and bound state binding energies from eigensates computed at finite lattice size is discussed.
Covariant diagrams for one-loop matching
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-10-15
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Batalin-Vilkovisky formalism in locally covariant field theory
Rejzner, Katarzyna
2011-01-01
The present work contains a complete formulation of the Batalin-Vilkovisky (BV) formalism in the framework of locally covariant field theory. In the first part of the thesis the classical theory is investigated with a particular focus on the infinite dimensional character of the underlying structures. It is shown that the use of infinite dimensional differential geometry allows for a conceptually clear and elegant formulation. The construction of the BV complex is performed in a fully covariant way and we also generalize the BV framework to a more abstract level, using functors and natural transformations. In this setting we construct the BV complex for classical gravity. This allows us to give a homological interpretation to the notion of diffeomorphism invariant physical quantities in general relativity. The second part of the thesis concerns the quantum theory. We provide a framework for the BV quantization that doesn't rely on the path integral formalism, but is completely formulated within perturbative a...
Globally covering a-priori regional gravity covariance models
Directory of Open Access Journals (Sweden)
D. Arabelos
2003-01-01
Full Text Available Gravity anomaly data generated using Wenzel’s GPM98A model complete to degree 1800, from which OSU91A has been subtracted, have been used to estimate covariance functions for a set of globally covering equal-area blocks of size 22.5° × 22.5° at Equator, having a 2.5° overlap. For each block an analytic covariance function model was determined. The models are based on 4 parameters: the depth to the Bjerhammar sphere (determines correlation, the free-air gravity anomaly variance, a scale factor of the OSU91A error degree-variances and a maximal summation index, N, of the error degree-variances. The depth of Bjerhammar-sphere varies from -134km to nearly zero, N varies from 360 to 40, the scale factor from 0.03 to 38.0 and the gravity variance from 1081 to 24(10µms-22. The parameters are interpreted in terms of the quality of the data used to construct OSU91A and GPM98A and general conditions such as the occurrence of mountain chains. The variation of the parameters show that it is necessary to use regional covariance models in order to obtain a realistic signal to noise ratio in global applications.Key words. GOCE mission, Covariance function, Spacewise approach`
Efficient retrieval of landscape Hessian: forced optimal covariance adaptive learning.
Shir, Ofer M; Roslund, Jonathan; Whitley, Darrell; Rabitz, Herschel
2014-06-01
Knowledge of the Hessian matrix at the landscape optimum of a controlled physical observable offers valuable information about the system robustness to control noise. The Hessian can also assist in physical landscape characterization, which is of particular interest in quantum system control experiments. The recently developed landscape theoretical analysis motivated the compilation of an automated method to learn the Hessian matrix about the global optimum without derivative measurements from noisy data. The current study introduces the forced optimal covariance adaptive learning (FOCAL) technique for this purpose. FOCAL relies on the covariance matrix adaptation evolution strategy (CMA-ES) that exploits covariance information amongst the control variables by means of principal component analysis. The FOCAL technique is designed to operate with experimental optimization, generally involving continuous high-dimensional search landscapes (≳30) with large Hessian condition numbers (≳10^{4}). This paper introduces the theoretical foundations of the inverse relationship between the covariance learned by the evolution strategy and the actual Hessian matrix of the landscape. FOCAL is presented and demonstrated to retrieve the Hessian matrix with high fidelity on both model landscapes and quantum control experiments, which are observed to possess nonseparable, nonquadratic search landscapes. The recovered Hessian forms were corroborated by physical knowledge of the systems. The implications of FOCAL extend beyond the investigated studies to potentially cover other physically motivated multivariate landscapes.
Hydrodynamic Covariant Symplectic Structure from Bilinear Hamiltonian Functions
Directory of Open Access Journals (Sweden)
Capozziello S.
2005-07-01
Full Text Available Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture. This feature is gauge free and it seems a deep link common to all interactions, electromagnetism and gravity included. This scheme could lead toward a full canonical quantization.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Micho Đurđevich; Stephen Bruce Sontz
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators amo...
Tonic and phasic co-variation of peripheral arousal indices in infants
Wass, S.V.; de Barbaro, K.; Clackson, K.
2015-01-01
Tonic and phasic differences in peripheral autonomic nervous system (ANS) indicators strongly predict differences in attention and emotion regulation in developmental populations. However, virtually all previous research has been based on individual ANS measures, which poses a variety of conceptual and methodlogical challenges to comparing results across studies. Here we recorded heart rate, electrodermal activity (EDA), pupil size, head movement velocity and peripheral accelerometry concurrently while a cohort of 37 typical 12-month-old infants completed a mixed assessment battery lasting approximately 20 min per participant. We analysed covariation of these autonomic indices in three ways: first, tonic (baseline) arousal; second, co-variation in spontaneous (phasic) changes during testing; third, phasic co-variation relative to an external stimulus event. We found that heart rate, head velocity and peripheral accelerometry showed strong positive co-variation across all three analyses. EDA showed no co-variation in tonic activity levels but did show phasic positive co-variation with other measures, that appeared limited to sections of high but not low general arousal. Tonic pupil size showed significant positive covariation, but phasic pupil changes were inconsistent. We conclude that: (i) there is high covariation between autonomic indices in infants, but that EDA may only be sensitive at extreme arousal levels, (ii) that tonic pupil size covaries with other indices, but does not show predicted patterns of phasic change and (iii) that motor activity appears to be a good proxy measure of ANS activity. The strongest patterns of covariation were observed using epoch durations of 40 s per epoch, although significant covariation between indices was also observed using shorter epochs (1 and 5 s). PMID:26316360
Into the Bulk: A Covariant Approach
Engelhardt, Netta
2016-01-01
I propose a general, covariant way of defining when one region is "deeper in the bulk" than another. This definition is formulated outside of an event horizon (or in the absence thereof) in generic geometries; it may be applied to both points and surfaces, and may be used to compare the depth of bulk points or surfaces relative to a particular boundary subregion or relative to the entire boundary. Using the recently proposed "lightcone cut" formalism, the comparative depth between two bulk points can be determined from the singularity structure of Lorentzian correlators in the dual field theory. I prove that, by this definition, causal wedges of progressively larger regions probe monotonically deeper in the bulk. The definition furthermore matches expectations in pure AdS and in static AdS black holes with isotropic spatial slices, where a well-defined holographic coordinate exists. In terms of holographic RG flow, this new definition of bulk depth makes contact with coarse-graining over both large distances ...
Schwinger mechanism in linear covariant gauges
Aguilar, A C; Papavassiliou, J
2016-01-01
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ans\\"atze. The gauge-dependent terms contributing to this ke...
Comparison between covariant and orthogonal Lyapunov vectors.
Yang, Hong-liu; Radons, Günter
2010-10-01
Two sets of vectors, covariant Lyapunov vectors (CLVs) and orthogonal Lyapunov vectors (OLVs), are currently used to characterize the linear stability of chaotic systems. A comparison is made to show their similarity and difference, especially with respect to the influence on hydrodynamic Lyapunov modes (HLMs). Our numerical simulations show that in both Hamiltonian and dissipative systems HLMs formerly detected via OLVs survive if CLVs are used instead. Moreover, the previous classification of two universality classes works for CLVs as well, i.e., the dispersion relation is linear for Hamiltonian systems and quadratic for dissipative systems, respectively. The significance of HLMs changes in different ways for Hamiltonian and dissipative systems with the replacement of OLVs with CLVs. For general dissipative systems with nonhyperbolic dynamics the long-wavelength structure in Lyapunov vectors corresponding to near-zero Lyapunov exponents is strongly reduced if CLVs are used instead, whereas for highly hyperbolic dissipative systems the significance of HLMs is nearly identical for CLVs and OLVs. In contrast the HLM significance of Hamiltonian systems is always comparable for CLVs and OLVs irrespective of hyperbolicity. We also find that in Hamiltonian systems different symmetry relations between conjugate pairs are observed for CLVs and OLVs. Especially, CLVs in a conjugate pair are statistically indistinguishable in consequence of the microreversibility of Hamiltonian systems. Transformation properties of Lyapunov exponents, CLVs, and hyperbolicity under changes of coordinate are discussed in appendices.
Covariance and objectivity in mechanics and turbulence
Frewer, Michael
2016-01-01
Form-invariance (covariance) and frame-indifference (objectivity) are two notions in classical continuum mechanics which have attracted much attention and controversy over the past decades. Particularly in turbulence modelling it seems that there still is a need for clarification. The aim and purpose of this study is fourfold: (i) To achieve consensus in general on definitions and principles when trying to establish an invariant theory for modelling constitutive structures and dynamic processes in mechanics, where special focus is put on the principle of Material Frame-Indifference (MFI). (ii) To show that in constitutive modelling MFI can only be regarded as an approximation that needs to be reduced to a weaker statement when trying to advance it to an axiom of nature. (iii) To convince that in dynamical modelling, as in turbulence, MFI may not be utilized as a modelling guideline, not even in an approximative sense. Instead, its reduced form has to be supplemented by a second, independent axiom that include...
Disintegrating the fly: A mutational perspective on phenotypic integration and covariation.
Haber, Annat; Dworkin, Ian
2017-01-01
The structure of environmentally induced phenotypic covariation can influence the effective strength and magnitude of natural selection. Yet our understanding of the factors that contribute to and influence the evolutionary lability of such covariation is poor. Most studies have either examined environmental variation without accounting for covariation, or examined phenotypic and genetic covariation without distinguishing the environmental component. In this study, we examined the effect of mutational perturbations on different properties of environmental covariation, as well as mean shape. We use strains of Drosophila melanogaster bearing well-characterized mutations known to influence wing shape, as well as naturally derived strains, all reared under carefully controlled conditions and with the same genetic background. We find that mean shape changes more freely than the covariance structure, and that different properties of the covariance matrix change independently from each other. The perturbations affect matrix orientation more than they affect matrix eccentricity or total variance. Yet, mutational effects on matrix orientation do not cluster according to the developmental pathway that they target. These results suggest that it might be useful to consider a more general concept of "decanalization," involving all aspects of variation and covariation.
Forecasting Covariance Matrices: A Mixed Frequency Approach
DEFF Research Database (Denmark)
Halbleib, Roxana; Voev, Valeri
This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...... matrix dynamics. Our empirical results show that the new mixing approach provides superior forecasts compared to multivariate volatility specifications using single sources of information....
Estimation of Low-Rank Covariance Function
Koltchinskii, Vladimir; Lounici, Karim; Tsybakov, Alexander B.
2015-01-01
We consider the problem of estimating a low rank covariance function $K(t,u)$ of a Gaussian process $S(t), t\\in [0,1]$ based on $n$ i.i.d. copies of $S$ observed in a white noise. We suggest a new estimation procedure adapting simultaneously to the low rank structure and the smoothness of the covariance function. The new procedure is based on nuclear norm penalization and exhibits superior performances as compared to the sample covariance function by a polynomial factor in the sample size $n$...
Generally covariant vs. gauge structure for conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Campigotto, M., E-mail: martacostanza.campigotto@to.infn.it [Dipartimento di Fisica, University of Torino, Via P. Giuria 1, 10125, Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Via P. Giuria 1, 10125, Torino (Italy); Fatibene, L. [Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123, Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Via P. Giuria 1, 10125, Torino (Italy)
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
Livshits, Gideon I
2014-01-01
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either th...
General covariant conservative angular momentum as internal charges
Institute of Scientific and Technical Information of China (English)
赵德品
1996-01-01
The usual approach to internal conservative charges is used to obtain the conservation laws of angular-momentum in both Einstein gravity and gravitational anyons.The results are in complete agreement with those of references.
Covariance NMR spectroscopy by singular value decomposition.
Trbovic, Nikola; Smirnov, Serge; Zhang, Fengli; Brüschweiler, Rafael
2004-12-01
Covariance NMR is demonstrated for homonuclear 2D NMR data collected using the hypercomplex and TPPI methods. Absorption mode 2D spectra are obtained by application of the square-root operation to the covariance matrices. The resulting spectra closely resemble the 2D Fourier transformation spectra, except that they are fully symmetric with the spectral resolution along both dimensions determined by the favorable resolution achievable along omega2. An efficient method is introduced for the calculation of the square root of the covariance spectrum by applying a singular value decomposition (SVD) directly to the mixed time-frequency domain data matrix. Applications are shown for 2D NOESY and 2QF-COSY data sets and computational benchmarks are given for data matrix dimensions typically encountered in practice. The SVD implementation makes covariance NMR amenable to routine applications.
Earth Observing System Covariance Realism Updates
Ojeda Romero, Juan A.; Miguel, Fred
2017-01-01
This presentation will be given at the International Earth Science Constellation Mission Operations Working Group meetings June 13-15, 2017 to discuss the Earth Observing System Covariance Realism updates.
Covariant Quantization with Extended BRST Symmetry
Geyer, B; Lavrov, P M
1999-01-01
A short rewiev of covariant quantization methods based on BRST-antiBRST symmetry is given. In particular problems of correct definition of Sp(2) symmetric quantization scheme known as triplectic quantization are considered.
Conformally covariant parametrizations for relativistic initial data
Delay, Erwann
2017-01-01
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parametrization is certainly more natural for non constant mean curvature initial data.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Covariate analysis of bivariate survival data
Energy Technology Data Exchange (ETDEWEB)
Bennett, L.E.
1992-01-01
The methods developed are used to analyze the effects of covariates on bivariate survival data when censoring and ties are present. The proposed method provides models for bivariate survival data that include differential covariate effects and censored observations. The proposed models are based on an extension of the univariate Buckley-James estimators which replace censored data points by their expected values, conditional on the censoring time and the covariates. For the bivariate situation, it is necessary to determine the expectation of the failure times for one component conditional on the failure or censoring time of the other component. Two different methods have been developed to estimate these expectations. In the semiparametric approach these expectations are determined from a modification of Burke's estimate of the bivariate empirical survival function. In the parametric approach censored data points are also replaced by their conditional expected values where the expected values are determined from a specified parametric distribution. The model estimation will be based on the revised data set, comprised of uncensored components and expected values for the censored components. The variance-covariance matrix for the estimated covariate parameters has also been derived for both the semiparametric and parametric methods. Data from the Demographic and Health Survey was analyzed by these methods. The two outcome variables are post-partum amenorrhea and breastfeeding; education and parity were used as the covariates. Both the covariate parameter estimates and the variance-covariance estimates for the semiparametric and parametric models will be compared. In addition, a multivariate test statistic was used in the semiparametric model to examine contrasts. The significance of the statistic was determined from a bootstrap distribution of the test statistic.
Covariant action for type IIB supergravity
Sen, Ashoke
2016-07-01
Taking clues from the recent construction of the covariant action for type II and heterotic string field theories, we construct a manifestly Lorentz covariant action for type IIB supergravity, and discuss its gauge fixing maintaining manifest Lorentz invariance. The action contains a (non-gravitating) free 4-form field besides the usual fields of type IIB supergravity. This free field, being completely decoupled from the interacting sector, has no physical consequence.
Functional CLT for sample covariance matrices
Bai, Zhidong; Zhou, Wang; 10.3150/10-BEJ250
2010-01-01
Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including $[(1-\\sqrt{y})^2,(1+\\sqrt{y})^2]$, the support of the Mar\\u{c}enko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.
On the covariance of residual lives
Directory of Open Access Journals (Sweden)
N. Unnikrishnan Nair
2007-10-01
Full Text Available Various properties of residual life such as mean, median, percentiles, variance etc have been discussed in literature on reliability and survival analysis. However a detailed study on covariance between residual lives in a two component system does not seem to have been undertaken. The present paper discusses various properties of product moment and covariance of residual lives. Relationships the product moment has with mean residual life and failure rate are studied and some characterizations are established.
Covariant Hamilton equations for field theory
Energy Technology Data Exchange (ETDEWEB)
Giachetta, Giovanni [Department of Mathematics and Physics, University of Camerino, Camerino (Italy); Mangiarotti, Luigi [Department of Mathematics and Physics, University of Camerino, Camerino (Italy)]. E-mail: mangiaro@camserv.unicam.it; Sardanashvily, Gennadi [Department of Theoretical Physics, Physics Faculty, Moscow State University, Moscow (Russian Federation)]. E-mail: sard@grav.phys.msu.su
1999-09-24
We study the relations between the equations of first-order Lagrangian field theory on fibre bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. If a Lagrangian is hyperregular, these equations are equivalent. A degenerate Lagrangian requires a set of associated Hamiltonian forms in order to exhaust all solutions of the Euler-Lagrange equations. The case of quadratic degenerate Lagrangians is studied in detail. (author)
Economical Phase-Covariant Cloning of Qudits
Buscemi, F; Macchiavello, C; Buscemi, Francesco; Ariano, Giacomo Mauro D'; Macchiavello, Chiara
2004-01-01
We derive the optimal $N\\to M$ phase-covariant quantum cloning for equatorial states in dimension $d$ with $M=kd+N$, $k$ integer. The cloning maps are optimal for both global and single-qudit fidelity. The map is achieved by an ``economical'' cloning machine, which works without ancilla. The connection between optimal phase-covariant cloning and optimal multi-phase estimation is finally established.
Transformation rule for covariance matrices under Bell-like detections
Spedalieri, Gaetana; Pirandola, Stefano
2013-01-01
Starting from the transformation rule of a covariance matrix under homodyne detections, we can easily derive a formula for the transformation of a covariance matrix of (n+2) bosonic modes under Bell-like detections, where the last two modes are combined in an arbitrary beam splitter (i.e., with arbitrary transmissivity) and then homodyned. This formula can be specialized to describe the standard Bell detection and the heterodyne measurement, which are exploited in many contexts, including protocols of quantum teleportation, entanglement swapping and quantum cryptography. Our general formula can be adopted to study these protocols in the presence of experimental imperfections or asymmetric setups, e.g., deriving from the use of unbalanced beam splitters.
Markov modulated Poisson process models incorporating covariates for rainfall intensity.
Thayakaran, R; Ramesh, N I
2013-01-01
Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.
Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
Lukierski, Jerzy
2015-01-01
We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \\mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H. The standard (4+4) -dimensional kappa - deformed covariant quantum phase space spanned by kappa - deformed Minkowski coordinates and commuting momenta generators ({x}_{\\mu },{p}_{\\mu }) is obtained as the subalgebra of \\mathcal{H}. We study further the property that Heisenberg double defines particular quantum spaces with Hopf algebroid structure. We calculate by using purely algebraic methods the explicite Hopf algebroid structure of standard kappa - deformed quantum covariant phase space in Majid-Ruegg bicrossproduct basis. The coproducts for Hopf algebroids are not unique, determined modulo the coproduct gauge freedom. Finally we consider the interpretation of the algebraic description of quantum phase spaces as Hopf bialgebroids.
Representations of Inverse Covariances by Differential Operators
Institute of Scientific and Technical Information of China (English)
Qin XU
2005-01-01
In the cost function of three- or four-dimensional variational data assimilation, each term is weighted by the inverse of its associated error covariance matrix and the background error covariance matrix is usually much larger than the other covariance matrices. Although the background error covariances are traditionally normalized and parameterized by simple smooth homogeneous correlation functions, the covariance matrices constructed from these correlation functions are often too large to be inverted or even manipulated. It is thus desirable to find direct representations of the inverses of background errorcorrelations. This problem is studied in this paper. In particular, it is shown that the background term can be written into ∫ dx|Dv(x)|2, that is, a squared L2 norm of a vector differential operator D, called the D-operator, applied to the field of analysis increment v(x). For autoregressive correlation functions, the Doperators are of finite orders. For Gaussian correlation functions, the D-operators are of infinite order. For practical applications, the Gaussian D-operators must be truncated to finite orders. The truncation errors are found to be small even when the Gaussian D-operators are truncated to low orders. With a truncated D-operator, the background term can be easily constructed with neither inversion nor direct calculation of the covariance matrix. D-operators are also derived for non-Gaussian correlations and transformed into non-isotropic forms.
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Meta-Analysis With a Continuous Covariate That Is Differentially Categorized Across Studies.
Perin, Jamie; Fischer Walker, Christa L; Black, Robert E; Aryee, Martin J
2016-03-01
We propose taking advantage of methodology for missing data to estimate relationships and adjust outcomes in a meta-analysis where a continuous covariate is differentially categorized across studies. The proposed method incorporates all available data in an implementation of the expectation-maximization algorithm. We use simulations to demonstrate that the proposed method eliminates bias that would arise by ignoring a covariate and generalizes the meta-analytical approach for incorporating covariates that are not uniformly categorized. The proposed method is illustrated in an application for estimating diarrhea incidence in children aged ≤59 months.
Flavour covariant transport equations: An application to resonant leptogenesis
Directory of Open Access Journals (Sweden)
P.S. Bhupal Dev
2014-09-01
Full Text Available We present a fully flavour-covariant formalism for transport phenomena, by deriving Markovian master equations that describe the time-evolution of particle number densities in a statistical ensemble with arbitrary flavour content. As an application of this general formalism, we study flavour effects in a scenario of resonant leptogenesis (RL and obtain the flavour-covariant evolution equations for heavy-neutrino and lepton number densities. This provides a complete and unified description of RL, capturing three distinct physical phenomena: (i the resonant mixing between the heavy-neutrino states, (ii coherent oscillations between different heavy-neutrino flavours, and (iii quantum decoherence effects in the charged-lepton sector. To illustrate the importance of this formalism, we numerically solve the flavour-covariant rate equations for a minimal RL model and show that the total lepton asymmetry can be enhanced by up to one order of magnitude, as compared to that obtained from flavour-diagonal or partially flavour off-diagonal rate equations. Thus, the viable RL model parameter space is enlarged, thereby enhancing further the prospects of probing a common origin of neutrino masses and the baryon asymmetry in the Universe at the LHC, as well as in low-energy experiments searching for lepton flavour and number violation. The key new ingredients in our flavour-covariant formalism are rank-4 rate tensors, which are required for the consistency of our flavour-mixing treatment, as shown by an explicit calculation of the relevant transition amplitudes by generalizing the optical theorem. We also provide a geometric and physical interpretation of the heavy-neutrino degeneracy limits in the minimal RL scenario. Finally, we comment on the consistency of various suggested forms for the heavy-neutrino self-energy regulator in the lepton-number conserving limit.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory
Ohsaku, Tadafumi
2013-01-01
The anomalous Nambu-Goldstone (NG) theorem which is found as a violation of counting law of the number of NG bosons of the normal NG theorem in nonrelativistic and Lorentz-symmetry-violated relativistic theories is studied in detail, with emphasis on its mathematical aspect from Lie algebras, geometry to number theory. The basis of counting law of NG bosons in the anomalous NG theorem is examined by Lie algebras (local) and Lie groups (global). A quasi-Heisenberg algebra is found generically in various symmetry breaking schema of the anomalous NG theorem, and it indicates that it causes a violation/modification of the Heisenberg uncertainty relation in an NG sector which can be experimentally confirmed. The formalism of effective potential is presented for understanding the mechanism of anomalous NG theorem with the aid of our result of Lie algebras. After an investigation on a bosonic kaon condensation model with a finite chemical potential as an explicit Lorentz-symmetry-breaking parameter, a model Lagrangi...
Energy Technology Data Exchange (ETDEWEB)
Goncalves, Bruno; Dias Junior, Mario Marcio [Instituto Federal de Educacacao, Ciencia e Tecnologia Sudeste de Minas Gerais, Juiz de Fora, MG (Brazil)
2013-07-01
Full text: The discussion of experimental manifestations of torsion at low energies is mainly related to the torsion-spin interaction. In this respect the behavior of Dirac field and the spinning particle in an external torsion field deserves and received very special attention. In this work, we consider the combined action of torsion and magnetic field on the massive spinor field. In this case, the Dirac equation is not straightforward solved. We suppose that the spinor has two components. The equations have mixed terms between the two components. The electromagnetic field is introduced in the action by the usual gauge transformation. The torsion field is described by the field S{sub μ}. The main purpose of the work is to get an explicit form to the equation of motion that shows the possible interactions between the external fields and the spinor in a Hamiltonian that is independent to each component. We consider that S{sub 0} is constant and is the unique non-vanishing term of S{sub μ}. This simplification is taken just to simplify the algebra, as our main point is not to describe the torsion field itself. In order to get physical analysis of the problem, we consider the non-relativistic approximation. The final result is a Hamiltonian that describes a half spin field in the presence of electromagnetic and torsion external fields. (author)
Effects of high-order operators in non-relativistic Lifshitz holography
Wang, Xinwen; Tian, Miao; Wang, Anzhong; Deng, Yanbin; Cleaver, Gerald
2014-01-01
In this paper, we study the effects of high-order operators on the non-relativistic Lifshitz holography in the framework of the Ho\\v{r}ava-Lifshitz (HL) theory of gravity, which naturally contains high-order operators in order for the theory to be power-counting renormalizble, and provides an ideal place to study these effects. In particular, we show that the Lifshitz space-time is still a solution of the full theory of the HL gravity. The effects of the high-oder operators on the space-time itself is simply to shift the Lifshitz dynamical exponent. However, while in the infrared the asymptotic behavior of a (probe) scalar field near the boundary is similar to that studied in the literature, it gets dramatically modified in the UV limit, because of the presence of the high-order operators in this regime. Then, according to the gauge/gravity duality, this in turn affects the two-point correlation functions.
Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
Nitta, Muneto; Vinci, Walter
2014-01-01
Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) x U(2) symmetry. We first show, at the classical level, the existence of S^3 = S^1 |x S^2 (S^1 fibered over S^2) NG modes associated to the breaking U(2) -> U(1) on vortices, where S^1 and S^2 correspond to type I and II NG modes, respectively. We th...
Stepanov, Nikolay S.; Zelekson, Lev A.
2017-03-01
The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams.
Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity
Hartong, Jelle; Lei, Yang; Obers, Niels A.
2016-09-01
We show that certain three-dimensional Hořava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various nonrelativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schrödinger algebras each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Hořava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Hořava-Lifshitz gravity with a local U (1 ) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schrödinger algebra containing three extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of nonprojectable conformal Hořava-Lifshitz gravity that we refer to as Chern-Simons Schrödinger gravity. This theory has a z =2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.
Accurate determination of the free-free Gaunt factor; I - non-relativistic Gaunt factors
van Hoof, P A M; Volk, K; Chatzikos, M; Ferland, G J; Lykins, M; Porter, R L; Wang, Y
2014-01-01
Modern spectral synthesis codes need the thermally averaged free-free Gaunt factor defined over a very wide range of parameter space in order to produce an accurate prediction for the spectrum emitted by an ionized plasma. Until now no set of data exists that would meet this need in a fully satisfactory way. We have therefore undertaken to produce a table of very accurate non-relativistic Gaunt factors over a much wider range of parameters than has ever been produced before. We first produced a table of non-averaged Gaunt factors, covering the parameter space log10(epsilon_i) = -20 to +10 and log10(w) = -30 to +25. We then continued to produce a table of thermally averaged Gaunt factors covering the parameter space log10(gamma^2) = -6 to +10 and log10(u) = -16 to +13. Finally we produced a table of the frequency integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to +10. All the data presented in this paper are available online.
Simulations of ion acceleration at non-relativistic shocks: i) Acceleration efficiency
Caprioli, Damiano
2013-01-01
We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfv\\'enic Mach numbers, produces universal power-law spectra proportional to p^(-4), where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10-20% of the bulk kinetic energy can be converted to energetic particles, and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration, and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shoc...
``Pheudo-cyclotron'' radiation of non-relativistic particles in small-scale magnetic turbulence
Keenan, Brett; Ford, Alex; Medvedev, Mikhail V.
2014-03-01
Plasma turbulence in some astrophysical objects (e.g., weakly magnetized collisionless shocks in GRBs and SN) has small-scale magnetic field fluctuations. We study spectral characteristics of radiation produced by particles moving in such turbulence. It was shown earlier that relativistic particles produce jitter radiation, which spectral characteristics are markedly different from synchrotron radiation. Here we study radiation produced by non-relativistic particles. In the case of a homogeneous fields, such radiation is cyclotron and its spectrum consists of just a single harmonic at the cyclotron frequency. However, in the sub-Larmor-scale turbulence, the radiation spectrum is much reacher and reflects statistical properties of the underlying magnetic field. We present both analytical estimates and results of ab initio numerical simulations. We also show that particle propagation in such turbulence is diffusive and evaluate the diffusion coefficient. We demonstrate that the diffusion coefficient correlates with some spectral parameters. These results can be very valuable for remote diagnostics of laboratory and astrophysical plasmas. Supported by grant DOE grant DE-FG02-07ER54940 and NSF grant AST-1209665.
AdS and dS black hole solutions in analogue gravity: The relativistic and non-relativistic cases
Dey, Ramit; Turcati, Rodrigo
2016-01-01
We show that Schwarzschild black hole solutions in asymptotically Anti-de Sitter (AdS) and de Sitter (dS) spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and non-relativistic Bose-Einstein condensates. In addition, we demonstrate that the (2+1) planar AdS black hole can be mapped into the non-relativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/gravity duality, we then comment on the possibility to study the AdS/CFT correspondence and gravity/fluid duality from an analogue gravity perspective.
Momentum and charge transport in non-relativistic holographic fluids from Ho\\v{r}ava gravity
Davison, Richard A; Janiszewski, Stefan; Kaminski, Matthias
2016-01-01
We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Ho\\v{r}ava gravity with Lifshitz exponent $z=1$. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Ho\\v{r}ava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Ho\\v{r}ava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.
Asymptotic behavior of the likelihood function of covariance matrices of spatial Gaussian processes
DEFF Research Database (Denmark)
Zimmermann, Ralf
2010-01-01
The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood......: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training...
Hawking radiation from the dilaton-(anti) de Sitter black hole via covariant anomaly
Institute of Scientific and Technical Information of China (English)
Han Yi-Wen; Bao Zhi-Qing; Hong Yun
2009-01-01
Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton-(anti) de Sitter black hole. To save the underlying gauge and general covariance, it introduces covariant fluxes of gauge and energy-momentum tensor to cancel the gauge and gravitational anomalies. The result shows that the introduced compensating fluxes are equivalent to those of a 2-dimensional blackbody radiation at Hawking temperature with appropriate chemical potential.
Coincidence and covariance data acquisition in photoelectron and -ion spectroscopy. I. Formal theory
Mikosch, Jochen; Patchkovskii, Serguei
2013-10-01
We derive a formal theory of noisy Poisson processes with multiple outcomes. We obtain simple, compact expressions for the probability distribution function of arbitrarily complex composite events and its moments. We illustrate the utility of the theory by analyzing properties of coincidence and covariance photoelectron-photoion detection involving single-ionization events. The results and techniques introduced in this work are directly applicable to more general coincidence and covariance experiments, including multiple ionization and multiple-ion fragmentation pathways.
Kobayashi, Michikazu
2014-01-01
We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in non-relativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) sigma model, a magnetic domain wall in ferromagnets with an easy axis.
Palge, Veiko; Dunningham, Jacob; Hasegawa, Yuji
2016-01-01
In quantum physics Wigner's rotation is commonly regarded as confirmed by the Thomas precession in a hydrogen like atom. In this paper we show that a direct experimental verification of Wigner's rotation is in principle accessible in the regime of non-relativistic velocities at $2 \\cdot 10^3\\,$m/s and propose an experiment using thermal neutrons. The experiment can be carried out in a laboratory and it provides a test of relativity in the quantum domain.
Recurrence Analysis of Eddy Covariance Fluxes
Lange, Holger; Flach, Milan; Foken, Thomas; Hauhs, Michael
2015-04-01
The eddy covariance (EC) method is one key method to quantify fluxes in biogeochemical cycles in general, and carbon and energy transport across the vegetation-atmosphere boundary layer in particular. EC data from the worldwide net of flux towers (Fluxnet) have also been used to validate biogeochemical models. The high resolution data are usually obtained at 20 Hz sampling rate but are affected by missing values and other restrictions. In this contribution, we investigate the nonlinear dynamics of EC fluxes using Recurrence Analysis (RA). High resolution data from the site DE-Bay (Waldstein-Weidenbrunnen) and fluxes calculated at half-hourly resolution from eight locations (part of the La Thuile dataset) provide a set of very long time series to analyze. After careful quality assessment and Fluxnet standard gapfilling pretreatment, we calculate properties and indicators of the recurrent structure based both on Recurrence Plots as well as Recurrence Networks. Time series of RA measures obtained from windows moving along the time axis are presented. Their interpretation is guided by three different questions: (1) Is RA able to discern periods where the (atmospheric) conditions are particularly suitable to obtain reliable EC fluxes? (2) Is RA capable to detect dynamical transitions (different behavior) beyond those obvious from visual inspection? (3) Does RA contribute to an understanding of the nonlinear synchronization between EC fluxes and atmospheric parameters, which is crucial for both improving carbon flux models as well for reliable interpolation of gaps? (4) Is RA able to recommend an optimal time resolution for measuring EC data and for analyzing EC fluxes? (5) Is it possible to detect non-trivial periodicities with a global RA? We will demonstrate that the answers to all five questions is affirmative, and that RA provides insights into EC dynamics not easily obtained otherwise.
Schwinger mechanism in linear covariant gauges
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2017-02-01
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modeled by means of certain physically motivated Ansätze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansätze are compatible with the existence of nontrivial solutions. When such Ansätze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing," while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.
A Plethora of Negative-Refraction Phenomenons in Relativistic and Non-Relativistic Scenarios
Mackay, Tom G
2010-01-01
In accordance with Snel's law of refraction, whether a plane wave is refracted in the negative sense or positive sense at a planar boundary between two homogenous mediums is determined solely by the orientation of the real parts of the wavevectors involved. Thus, negative refraction should be distinguished from the associated but independent phenomenons of negative phase velocity, counterposition and negative deflection of energy flux. None of these phenomenons is Lorentz covariant.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Energy Technology Data Exchange (ETDEWEB)
Abłamowicz, Rafał, E-mail: rablamowicz@tntech.edu [Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, Tennessee 38505 (United States); Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br [Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP (Brazil); Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy)
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
MIMO Radar Transmit Beampattern Design Without Synthesising the Covariance Matrix
Ahmed, Sajid
2013-10-28
Compared to phased-array, multiple-input multiple-output (MIMO) radars provide more degrees-offreedom (DOF) that can be exploited for improved spatial resolution, better parametric identifiability, lower side-lobe levels at the transmitter/receiver, and design variety of transmit beampatterns. The design of the transmit beampattern generally requires the waveforms to have arbitrary auto- and crosscorrelation properties. The generation of such waveforms is a two step complicated process. In the first step a waveform covariance matrix is synthesised, which is a constrained optimisation problem. In the second step, to realise this covariance matrix actual waveforms are designed, which is also a constrained optimisation problem. Our proposed scheme converts this two step constrained optimisation problem into a one step unconstrained optimisation problem. In the proposed scheme, in contrast to synthesising the covariance matrix for the desired beampattern, nT independent finite-alphabet constantenvelope waveforms are generated and pre-processed, with weight matrix W, before transmitting from the antennas. In this work, two weight matrices are proposed that can be easily optimised for the desired symmetric and non-symmetric beampatterns and guarantee equal average power transmission from each antenna. Simulation results validate our claims.
Wishart distributions for decomposable covariance graph models
Khare, Kshitij; 10.1214/10-AOS841
2011-01-01
Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also referred to as Gaussian graphical models or covariance selection models) since the zeros in the parameter are now reflected in the covariance matrix $\\Sigma$, as compared to the concentration matrix $\\Omega =\\Sigma^{-1}$. The parameter space of interest for covariance graph models is the cone $P_G$ of positive definite matrices with fixed zeros corresponding to the missing edges of $G$. As in Letac and Massam [Ann. Statist. 35 (2007) 1278--1323], we consider the case where $G$ is decomposable. In this paper, we construct on the cone $P_G$ a family of Wishart distributions which serve a similar purpose in the covariance graph setting as those constructed by Letac and Massam [Ann. Statist. 35 (2007) 1278--1323] and Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272--1317] do in ...
Cross-covariance functions for multivariate geostatistics
Genton, Marc G.
2015-05-01
Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems. © Institute of Mathematical Statistics, 2015.
Lorentz covariance of loop quantum gravity
Rovelli, Carlo
2010-01-01
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This c...
Revisiting Gruss's inequality: covariance bounds,QDE but not QD copulas, and central moments
Egozcue, Martin; Wong, Wing-Keung; Zitikis, Ricardas
2010-01-01
Since the pioneering work of Gerhard Gruss dating back to 1935, Gruss's inequality and, more generally, Gruss-type bounds for covariances have fascinated researchers and found numerous applications in areas such as economics, insurance, reliability, and, more generally, decision making under uncertainly. Gruss-type bounds for covariances have been established mainly under most general dependence structures, meaning no restrictions on the dependence structure between the two underlying random variables. Recent work in the area has revealed a potential for improving Gruss-type bounds, including the original Gruss's bound, assuming dependence structures such as quadrant dependence (QD). In this paper we demonstrate that the relatively little explored notion of `quadrant dependence in expectation' (QDE) is ideally suited in the context of bounding covariances, especially those that appear in the aforementioned areas of application. We explore this research avenue in detail, establish general Gruss-type bounds, an...
Progress on Nuclear Data Covariances: AFCI-1.2 Covariance Library
Energy Technology Data Exchange (ETDEWEB)
Oblozinsky,P.; Oblozinsky,P.; Mattoon,C.M.; Herman,M.; Mughabghab,S.F.; Pigni,M.T.; Talou,P.; Hale,G.M.; Kahler,A.C.; Kawano,T.; Little,R.C.; Young,P.G
2009-09-28
Improved neutron cross section covariances were produced for 110 materials including 12 light nuclei (coolants and moderators), 78 structural materials and fission products, and 20 actinides. Improved covariances were organized into AFCI-1.2 covariance library in 33-energy groups, from 10{sup -5} eV to 19.6 MeV. BNL contributed improved covariance data for the following materials: {sup 23}Na and {sup 55}Mn where more detailed evaluation was done; improvements in major structural materials {sup 52}Cr, {sup 56}Fe and {sup 58}Ni; improved estimates for remaining structural materials and fission products; improved covariances for 14 minor actinides, and estimates of mubar covariances for {sup 23}Na and {sup 56}Fe. LANL contributed improved covariance data for {sup 235}U and {sup 239}Pu including prompt neutron fission spectra and completely new evaluation for {sup 240}Pu. New R-matrix evaluation for {sup 16}O including mubar covariances is under completion. BNL assembled the library and performed basic testing using improved procedures including inspection of uncertainty and correlation plots for each material. The AFCI-1.2 library was released to ANL and INL in August 2009.
Accurate covariance estimation of galaxy-galaxy weak lensing: limitations of jackknife covariance
Shirasaki, Masato; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma
2016-01-01
We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations. We populate a real catalog of source galaxies into a light-cone simulation realization, simulate the lensing effect on each galaxy, and then identify lensing halos that are considered to host galaxies or clusters of interest. We use the mock catalog to study the error covariance matrix of galaxy-galaxy weak lensing and find that the super-sample covariance (SSC), which arises from density fluctuations with length scales comparable with or greater than a size of survey area, gives a dominant source of the sample variance. We then compare the full covariance with the jackknife (JK) covariance, the method that estimates the covariance from the resamples of the data itself. We show that, although the JK method gives an unbiased estimator of the covariance in the shot noise or Gaussian regime, it always over-estimates the true covariance in the sample variance regime, because the JK covariance turns out to be a...
Activities on covariance estimation in Japanese Nuclear Data Committee
Energy Technology Data Exchange (ETDEWEB)
Shibata, Keiichi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1997-03-01
Described are activities on covariance estimation in the Japanese Nuclear Data Committee. Covariances are obtained from measurements by using the least-squares methods. A simultaneous evaluation was performed to deduce covariances of fission cross sections of U and Pu isotopes. A code system, KALMAN, is used to estimate covariances of nuclear model calculations from uncertainties in model parameters. (author)
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
Gomes, Henrique
2017-09-01
In an accompanying paper Gomes (arXiv:1504.02818, 2015), we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space Q of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, M-O, if the projection of extremal curves on Q onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to e^{i\\hat{H}t}circ prO= prOcirc e^{i\\hat{H}t}, where prO:Q→ Q_O^{partial O} is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality.
A covariant formulation of classical spinning particle
Cho, J H; Kim, J K; Jin-Ho Cho; Seungjoon Hyun; Jae-Kwan Kim
1994-01-01
Covariantly we reformulate the description of a spinning particle in terms of the which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame and not just from the particle rest frame. In distinction with the usual formulation, our system is directly comparable with the pseudo-classical formulation. We get a peculiar symmetry which resembles the supersymmetry of the pseudo-classical formulation.
A violation of the covariant entropy bound?
Masoumi, Ali
2014-01-01
Several arguments suggest that the entropy density at high energy density $\\rho$ should be given by the expression $s=K\\sqrt{\\rho/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by $A/4G$, where $A$ is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for $s$ violates the covariant entropy bound. We consider different possible explanations for this fact; in particular the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.
Shen, Chung-Wei; Chen, Yi-Hau
2015-10-01
Missing observations and covariate measurement error commonly arise in longitudinal data. However, existing methods for model selection in marginal regression analysis of longitudinal data fail to address the potential bias resulting from these issues. To tackle this problem, we propose a new model selection criterion, the Generalized Longitudinal Information Criterion, which is based on an approximately unbiased estimator for the expected quadratic error of a considered marginal model accounting for both data missingness and covariate measurement error. The simulation results reveal that the proposed method performs quite well in the presence of missing data and covariate measurement error. On the contrary, the naive procedures without taking care of such complexity in data may perform quite poorly. The proposed method is applied to data from the Taiwan Longitudinal Study on Aging to assess the relationship of depression with health and social status in the elderly, accommodating measurement error in the covariate as well as missing observations.
Parametric methods for estimating covariate-dependent reference limits.
Virtanen, Arja; Kairisto, Veli; Uusipaikka, Esa
2004-01-01
Age-specific reference limits are required for many clinical laboratory measurements. Statistical assessment of calculated intervals must be performed to obtain reliable reference limits. When parametric, covariate-dependent limits are derived, normal distribution theory usually is applied due to its mathematical simplicity and relative ease of fitting. However, it is not always possible to transform data and achieve a normal distribution. Therefore, models other than those based on normal distribution theory are needed. Generalized linear model theory offers one such alternative. Regardless of the statistical model used, the assumptions behind the model should always be examined.
Second central extension in Galilean covariant field theory
Hagen, C R
2002-01-01
The second central extension of the planar Galilei group has been alleged to have its origin in the spin variable. This idea is explored here by considering local Galilean covariant field theory for free fields of arbitrary spin. It is shown that such systems generally display only a trivial realization of the second central extension. While it is possible to realize any desired value of the extension parameter by suitable redefinition of the boost operator, such an approach has no necessary connection to the spin of the basic underlying field.
Statistical mechanics of covariant systems with multi-fingered time
Chirco, Goffredo
2016-01-01
Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the J\\"uttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.
Representation of Gaussian semimartingales with applications to the covariance function
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2010-01-01
The present paper is concerned with various aspects of Gaussian semimartingales. Firstly, generalizing a result of Stricker, we provide a convenient representation of Gaussian semimartingales as an -semimartingale plus a process of bounded variation which is independent of M. Secondly, we study...... stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...
Poisson process Fock space representation, chaos expansion and covariance inequalities
Last, Guenter
2009-01-01
We consider a Poisson process $\\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\\eta$.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Durdevich, Micho; Sontz, Stephen Bruce
2013-05-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Directory of Open Access Journals (Sweden)
Micho Đurđevich
2013-05-01
Full Text Available A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
evich, Micho Đurđ
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutivity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Ridgely, Charles T.
2010-01-01
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…
Ridgely, Charles T.
2010-01-01
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…
Lee, Sik-Yum; Song, Xin-Yuan; Tang, Nian-Sheng
2007-01-01
The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a…
Wiesendanger, C
2011-01-01
Viewing gravitational energy-momentum $p_G^\\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\\mu$ naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space ${\\bf M}^{\\sl 4}$. To extract its physical content the full gauge group is reduced to its Poincar\\'e subgroup. The respective Poincar\\'e gauge fields, field strengths and Poincar\\'e-covariant field equations are obtained and point-particle source currents are derived. The resulting set of non-linear field equations coupled to point matter is solved in first order resulting in Lienard-Wiechert-like potentials for the Poincar\\'e fields. After numerical identification of gravitational and inertial energy-momentum Newton's inverse square law for gravity in the static non-relativistic limit is recovered. The Weak Equivalence Principle in this approximation is proven to be valid and spacetime geometry in the presence of Poincar\\'e fields is shown to be curved. Finally, the gravit...
The Massless Spectrum of Covariant Superstrings
Grassi, P A; van Nieuwenhuizen, P
2002-01-01
We obtain the correct cohomology at any ghost number for the open and closed covariant superstring, quantized by an approach which we recently developed. We define physical states by the usual condition of BRST invariance and a new condition involving a new current which is related to a grading of the underlying affine Lie algebra.
EQUIVALENT MODELS IN COVARIANCE STRUCTURE-ANALYSIS
LUIJBEN, TCW
1991-01-01
Defining equivalent models as those that reproduce the same set of covariance matrices, necessary and sufficient conditions are stated for the local equivalence of two expanded identified models M1 and M2 when fitting the more restricted model M0. Assuming several regularity conditions, the rank def
Optimal covariate designs theory and applications
Das, Premadhis; Mandal, Nripes Kumar; Sinha, Bikas Kumar
2015-01-01
This book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as such choices allow experimenters to extract maximum information for the unknown model parameters. The main emphasis of this monograph is to start with an assumed covariate model in combination with some standard ANOVA set-ups such as CRD, RBD, BIBD, GDD, BTIBD, BPEBD, cross-over, multi-factor, split-plot and strip-plot designs, treatment control designs, etc. and discuss the nature and availability of optimal covariate designs. In some situations, optimal estimations of both ANOVA and the regression parameters are provided. Global optimality and D-optimality criteria are mainly used in selecting the design. The standard optimality results of both discrete and continuous set-ups have been adapted, and several novel combinatorial techniques have been applied for...
Covariant formulation of pion-nucleon scattering
Lahiff, A. D.; Afnan, I. R.
A covariant model of elastic pion-nucleon scattering based on the Bethe-Salpeter equation is presented. The kernel consists of s- and u-channel nucleon and delta poles, along with rho and sigma exchange in the t-channel. A good fit is obtained to the s- and p-wave phase shifts up to the two-pion production threshold.
Approximate methods for derivation of covariance data
Energy Technology Data Exchange (ETDEWEB)
Tagesen, S. [Vienna Univ. (Austria). Inst. fuer Radiumforschung und Kernphysik; Larson, D.C. [Oak Ridge National Lab., TN (United States)
1992-12-31
Several approaches for the derivation of covariance information for evaluated nuclear data files (EFF2 and ENDF/B-VI) have been developed and used at IRK and ORNL respectively. Considerations, governing the choice of a distinct method depending on the quantity and quality of available data are presented, advantages/disadvantages are discussed and examples of results are given.
Covariance of noncommutative Grassmann star product
Daoud, M.
2004-01-01
Using the Coherent states of many fermionic degrees of freedom labeled by Gra\\ss mann variables, we introduce the noncommutative (precisely non anticommutative) Gra\\ss mann star product. The covariance of star product under unitary transformations, particularly canonical ones, is studied. The super star product, based on supercoherent states of supersymmetric harmonic oscillator, is also considered.
Covariance of the selfdual vector model
2004-01-01
The Poisson algebra between the fields involved in the vectorial selfdual action is obtained by means of the reduced action. The conserved charges associated with the invariance under the inhomogeneous Lorentz group are obtained and its action on the fields. The covariance of the theory is proved using the Schwinger-Dirac algebra. The spin of the excitations is discussed.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Linear transformations of variance/covariance matrices
Parois, P.J.A.; Lutz, M.
2011-01-01
Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance
Covariant Photon Quantization in the SME
Colladay, Don
2013-01-01
The Gupta Bleuler quantization procedure is applied to the SME photon sector. A direct application of the method to the massless case fails due to an unavoidable incompleteness in the polarization states. A mass term can be included into the photon lagrangian to rescue the quantization procedure and maintain covariance.
Covariant derivative expansion of the heat kernel
Energy Technology Data Exchange (ETDEWEB)
Salcedo, L.L. [Universidad de Granada, Departamento de Fisica Moderna, Granada (Spain)
2004-11-01
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four derivatives. The results apply to boundaryless flat space-times and arbitrary non-Abelian scalar and gauge background fields. (orig.)
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2004-01-01
This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing...... the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through time. In particular we provide confidence intervals for each of these quantities....
Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space-time construct are consistent with the existence of a dynamical 3-space, and absolute motion. We illustrate this mapping first with the standard theory of sound, as vibrations of a medium, which itself may be undergoing fluid motion, and which is covariant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under Lorentz transformations wherein the speed of sound is now the invariant speed. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian spacetime description of sound, with a metric characterised by an invariant speed of sound. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equations were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a allowing dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Unravelling Lorentz Covariance and the Spacetime Formalism
Directory of Open Access Journals (Sweden)
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space- time construct are consistent with the existence of a dynamical 3-space, and “absolute motion”. We illustrate this mapping first with the standard theory of sound, as vibra- tions of a medium, which itself may be undergoing fluid motion, and which is covari- ant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under “Lorentz transformations” wherein the speed of sound is now the “invariant speed”. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian “spacetime” description of sound, with a metric characterised by an “invariant speed of sound”. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equa- tions were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a “flowing” dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Agbemava, S E; Ring, P
2016-01-01
A systematic investigation of octupole deformed nuclei is presented for even-even systems with $Z\\leq 106$ located between the two-proton and two-neutron drip lines. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range. This allows us to assess theoretical uncertainties within the present covariant models for the prediction of physical observables relevant for octupole deformed nuclei. In addition, a detailed comparison with the predictions of non-relativistic models is performed. A new region of octupole deformation, centered around $Z\\sim 98, N\\sim 196$ is predicted for the first time. In terms of its size in the $(Z,N)$ plane and the impact of octupole deformation on binding e...
National Research Council Canada - National Science Library
John B Holmes; Ken G Dodds; Michael A Lee
2017-01-01
.... While various measures of connectedness have been proposed in the literature, there is general agreement that the most appropriate measure is some function of the prediction error variance-covariance matrix...
Persico, Franco; Power, Edwin A.
1988-01-01
The physics of the electromagnetic vacuum, its fluctuations and its role in spontaneous emission has been studied since the early days of the quantum theory of radiation. In recent years there has been a renewed interest in the nature of the vacuum state and its potency in giving rise to observable effects. For example the question of amplification of photon signals and the way vacuum fluctuations may provide inescapable noise is fundamental to the theory of measurement. Quantum electrodynamics in cavities has become a very active area of research both experimentally and theoretically and the way the radiation field, even in vacuo, is changed by confinement is of interest and importance. The effective Einstein A-coefficient can be much smaller than in free space because the available modes are sparser in a cavity. Radiative connections such as the Lamb shift energies are also changed as the virtual photon modes are varied by the confinement. The existence of electromagnetic field energy (from the vacuum fluctuations) in the neighbourhood of atoms/molecules in their ground state is demonstrated by its effect on test molecules brought into the vicinity of the original sources. All the forces analogous to that of Van der Waals, including of course their Casimir retardations at long range, are explicable in terms of these virtual cloud effects. The Adriatico Conference on "Vacuum in Non-Relativistic Matter-Radiation Systems" held in July 1987 brought together scientists in quantum optics, quantum field theorists and others interested in the electromagnetic vacuum. It was most successful in that the participants found enough mutual agreement but with clearly defined tensions between them to provide excitement and argument throughout the four days' meeting. This volume consists of most of the papers presented at the conference. It is clear that the collection ranges from the pedagogical and the review type article to research papers with original material. The
Energy Technology Data Exchange (ETDEWEB)
Sapir, Nir; Waxman, Eli [Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100 (Israel); Katz, Boaz [Institute for Advanced Study, Princeton, NJ 08540 (United States)
2013-09-01
The spectrum of radiation emitted following shock breakout from a star's surface with a power-law density profile {rho}{proportional_to}x{sup n} is investigated. Assuming planar geometry, local Compton equilibrium, and bremsstrahlung emission as the dominant photon production mechanism, numerical solutions are obtained for the photon number density and temperature profiles as a function of time for hydrogen-helium envelopes. The temperature solutions are determined by the breakout shock velocity v{sub 0} and the pre-shock breakout density {rho}{sub 0} and depend weakly on the value of n. Fitting formulae for the peak surface temperature at breakout as a function of v{sub 0} and {rho}{sub 0} are provided, with T{sub peak} approx. 9.44 exp [12.63(v{sub 0}/c){sup 1/2}] eV, and the time dependence of the surface temperature is tabulated. The time integrated emitted spectrum is a robust prediction of the model, determined by T{sub peak} and v{sub 0} alone and insensitive to details of light travel time or slight deviations from spherical symmetry. Adopting commonly assumed progenitor parameters, breakout luminosities of Almost-Equal-To 10{sup 45} erg s{sup -1} and Almost-Equal-To 10{sup 44} erg s{sup -1} in the 0.3-10 keV band are expected for blue supergiant (BSG) and red supergiant (RSG)/He-WR progenitors, respectively (T{sub peak} is well below the band for RSGs, unless their radius is {approx}10{sup 13} cm). >30 detections of SN 1987A-like (BSG) breakouts are expected over the lifetime of ROSAT and XMM-Newton. An absence of such detections would imply either that the typical parameters assumed for BSG progenitors are grossly incorrect or that their envelopes are not hydrostatic. The observed spectrum and duration of XRF 080109/SN 2008D are in tension with a non-relativistic breakout from a stellar surface interpretation.
OSp(1,2)-covariant Lagrangian quantization of irreducible massive gauge theories
Geyer, B; Mülsch, D
1997-01-01
The OSp(1,2)-covariant Lagrangian quantization of general gauge theories is formulated which applies also to massive gauge fields. The formalism generalizes the Sp(2)-covariant BLT approach and guarantees symplectic invariance of the quantized action. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case disappears in the limit m = 0. Ward identities related to OSp(1,2) symmetry are derived. Massive gauge theories with closed algebra are studied as an example.
Ding, Min; Li, Yachun
2017-04-01
We study the 1-D piston problem for the relativistic Euler equations under the assumption that the total variations of both the initial data and the velocity of the piston are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we consider the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic Euler equations as the light speed c→ +∞.
Janes, Holly; Pepe, Margaret S
2009-06-01
Recent scientific and technological innovations have produced an abundance of potential markers that are being investigated for their use in disease screening and diagnosis. In evaluating these markers, it is often necessary to account for covariates associated with the marker of interest. Covariates may include subject characteristics, expertise of the test operator, test procedures or aspects of specimen handling. In this paper, we propose the covariate-adjusted receiver operating characteristic curve, a measure of covariate-adjusted classification accuracy. Nonparametric and semiparametric estimators are proposed, asymptotic distribution theory is provided and finite sample performance is investigated. For illustration we characterize the age-adjusted discriminatory accuracy of prostate-specific antigen as a biomarker for prostate cancer.
Batalin-Vilkovisky formalism in locally covariant field theory
Energy Technology Data Exchange (ETDEWEB)
Rejzner, Katarzyna Anna
2011-12-15
The present work contains a complete formulation of the Batalin-Vilkovisky (BV) formalism in the framework of locally covariant field theory. In the first part of the thesis the classical theory is investigated with a particular focus on the infinite dimensional character of the underlying structures. It is shown that the use of infinite dimensional differential geometry allows for a conceptually clear and elegant formulation. The construction of the BV complex is performed in a fully covariant way and we also generalize the BV framework to a more abstract level, using functors and natural transformations. In this setting we construct the BV complex for classical gravity. This allows us to give a homological interpretation to the notion of diffeomorphism invariant physical quantities in general relativity. The second part of the thesis concerns the quantum theory. We provide a framework for the BV quantization that doesn't rely on the path integral formalism, but is completely formulated within perturbative algebraic quantum field theory. To make such a formulation possible we first prove that the renormalized time-ordered product can be understood as a binary operation on a suitable domain. Using this result we prove the associativity of this product and provide a consistent framework for the renormalized BV structures. In particular the renormalized quantum master equation and the renormalized quantum BV operator are defined. To give a precise meaning to theses objects we make a use of the master Ward identity, which is an important structure in causal perturbation theory. (orig.)
On the regularity of the covariance matrix of a discretized scalar field on the sphere
Bilbao-Ahedo, J. D.; Barreiro, R. B.; Herranz, D.; Vielva, P.; Martínez-González, E.
2017-02-01
We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.
A trade-off solution between model resolution and covariance in surface-wave inversion
Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.
2010-01-01
Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.
Multilevel covariance regression with correlated random effects in the mean and variance structure.
Quintero, Adrian; Lesaffre, Emmanuel
2017-09-01
Multivariate regression methods generally assume a constant covariance matrix for the observations. In case a heteroscedastic model is needed, the parametric and nonparametric covariance regression approaches can be restrictive in the literature. We propose a multilevel regression model for the mean and covariance structure, including random intercepts in both components and allowing for correlation between them. The implied conditional covariance function can be different across clusters as a result of the random effect in the variance structure. In addition, allowing for correlation between the random intercepts in the mean and covariance makes the model convenient for skewedly distributed responses. Furthermore, it permits us to analyse directly the relation between the mean response level and the variability in each cluster. Parameter estimation is carried out via Gibbs sampling. We compare the performance of our model to other covariance modelling approaches in a simulation study. Finally, the proposed model is applied to the RN4CAST dataset to identify the variables that impact burnout of nurses in Belgium. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
On covariance structure in noisy, big data
Paffenroth, Randy C.; Nong, Ryan; Du Toit, Philip C.
2013-09-01
Herein we describe theory and algorithms for detecting covariance structures in large, noisy data sets. Our work uses ideas from matrix completion and robust principal component analysis to detect the presence of low-rank covariance matrices, even when the data is noisy, distorted by large corruptions, and only partially observed. In fact, the ability to handle partial observations combined with ideas from randomized algorithms for matrix decomposition enables us to produce asymptotically fast algorithms. Herein we will provide numerical demonstrations of the methods and their convergence properties. While such methods have applicability to many problems, including mathematical finance, crime analysis, and other large-scale sensor fusion problems, our inspiration arises from applying these methods in the context of cyber network intrusion detection.
Covariant holography of a tachyonic accelerating universe
Rozas-Fernández, Alberto
2014-01-01
We apply the holographic principle to a flat dark energy dominated Friedmann-Robertson-Walker spacetime filled with a tachyon scalar field with constant equation of state $w=p/\\rho$, both for $w>-1$ and $w<-1$. By using a geometrical covariant procedure, which allows the construction of holographic hypersurfaces, we have obtained for each case the position of the preferred screen and have then compared these with those obtained by using the holographic dark energy model with the future event horizon as the infrared cutoff. In the phantom scenario, one of the two obtained holographic screens is placed on the big rip hypersurface, both for the covariant holographic formalism and the holographic phantom model. It is also analysed whether the existence of these preferred screens allows a mathematically consistent formulation of fundamental theories based on the existence of a S matrix at infinite distances.
Model selection for Poisson processes with covariates
Sart, Mathieu
2011-01-01
We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. To handle this problem, we assume that the intensity of each Poisson process is of the form $s (\\cdot, x)$ where $x$ is the covariate and where $s$ is an unknown function. We propose a model selection approach where the models are used to approximate the multivariate function $s$. We show that our estimator satisfies an oracle-type inequality under very weak assumptions both on the intensities and the models. By using an Hellinger-type loss, we establish non-asymptotic risk bounds and specify them under various kind of assumptions on the target function $s$ such as being smooth or composite. Besides, we show that our estimation procedure is robust with respect to these assumptions.
Errors on errors - Estimating cosmological parameter covariance
Joachimi, Benjamin
2014-01-01
Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly aware that these requirements not only apply to the central values of parameters but, equally important, also to the error bars. Due to non-linear effects in the astrophysics, the instrument, and the analysis pipeline, data covariance matrices are usually not well known a priori and need to be estimated from the data itself, or from suites of large simulations. In either case, the finite number of realisations available to determine data covariances introduces significant biases and additional variance in the errors on cosmological parameters in a standard likelihood analysis. Here, we review recent work on quantifying these biases and additional variances and discuss approaches to remedy these effects.
Linear transformations of variance/covariance matrices.
Parois, Pascal; Lutz, Martin
2011-07-01
Many applications in crystallography require the use of linear transformations on parameters and their standard uncertainties. While the transformation of the parameters is textbook knowledge, the transformation of the standard uncertainties is more complicated and needs the full variance/covariance matrix. For the transformation of second-rank tensors it is suggested that the 3 × 3 matrix is re-written into a 9 × 1 vector. The transformation of the corresponding variance/covariance matrix is then straightforward and easily implemented into computer software. This method is applied in the transformation of anisotropic displacement parameters, the calculation of equivalent isotropic displacement parameters, the comparison of refinements in different space-group settings and the calculation of standard uncertainties of eigenvalues.
Covariant holography of a tachyonic accelerating universe
Energy Technology Data Exchange (ETDEWEB)
Rozas-Fernandez, Alberto [Consejo Superior de Investigaciones Cientificas, Instituto de Fisica Fundamental, Madrid (Spain); University of Portsmouth, Institute of Cosmology and Gravitation, Portsmouth (United Kingdom)
2014-08-15
We apply the holographic principle to a flat dark energy dominated Friedmann-Robertson-Walker spacetime filled with a tachyon scalar field with constant equation of state w = p/ρ, both for w > -1 and w < -1. By using a geometrical covariant procedure, which allows the construction of holographic hypersurfaces, we have obtained for each case the position of the preferred screen and have then compared these with those obtained by using the holographic dark energy model with the future event horizon as the infrared cutoff. In the phantom scenario, one of the two obtained holographic screens is placed on the big rip hypersurface, both for the covariant holographic formalism and the holographic phantom model. It is also analyzed whether the existence of these preferred screens allows a mathematically consistent formulation of fundamental theories based on the existence of an S-matrix at infinite distances. (orig.)
Chiral Four-Dimensional Heterotic Covariant Lattices
Beye, Florian
2014-01-01
In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all right-mover lattices that can appear in such a chiral model, and to study the corresponding left-mover lattices using the theory of lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is employed to calculate a lower bound on the number of left-mover lattices. Also, the known relationship between asymmetric orbifolds and covariant lattices is considered in the context of our classification.
Covariant action for a string in doubled yet gauged spacetime
Lee, Kanghoon
2014-01-01
The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true and continue to explore the idea of `spacetime being doubled yet gauged'. Introducing an appropriate gauge connection, we construct a string action, with an arbitrary generalized metric, which is completely covariant with respect to the coordinate gauge symmetry, generalized diffeomorphisms, world-sheet diffeomorphisms and O(D,D) T-duality. A topological term previously proposed in the literature naturally arises and a self-duality condition follows from the equations of motion. Further, the action may couple to a T-dual background where the Riemannian metric becomes everywhere singular.
Distributed Remote Vector Gaussian Source Coding with Covariance Distortion Constraints
DEFF Research Database (Denmark)
Zahedi, Adel; Østergaard, Jan; Jensen, Søren Holdt
2014-01-01
In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a covariance matrix distortion constraint and in the presence...... of side information at the decoder. For this problem, we derive lower and upper bounds on the rate-distortion function (RDF) for the Gaussian case, which in general do not coincide. We then provide some cases, where the RDF can be derived exactly. We also show that previous results on specific instances...... of this problem can be generalized using our results. We finally show that if the distortion measure is the mean squared error, or if it is replaced by a certain mutual information constraint, the optimal rate can be derived from our main result....
Twisted Covariant Noncommutative Self-dual Gravity
Estrada-Jimenez, S; Obregón, O; Ramírez, C
2008-01-01
A twisted covariant formulation of noncommutative self-dual gravity is presented. The recent formulation introduced by J. Wess and coworkers for constructing twisted Yang-Mills fields is used. It is shown that the noncommutative torsion is solved at any order of the $\\theta$-expansion in terms of the tetrad and the extra fields of the theory. In the process the first order expansion in $\\theta$ for the Pleba\\'nski action is explicitly obtained.
Covariant quantization of the CBS superparticle
Energy Technology Data Exchange (ETDEWEB)
Grassi, P.A. E-mail: pag5@nyu.edu; Policastro, G.; Porrati, M
2001-07-09
The quantization of the Casalbuoni-Brink-Schwarz superparticle is performed in an explicitly covariant way using the antibracket formalism. Since an infinite number of ghost fields are required, within a suitable off-shell twistor-like formalism, we are able to fix the gauge of each ghost sector without modifying the physical content of the theory. The computation reveals that the antibracket cohomology contains only the physical degrees of freedom.
Economical phase-covariant cloning with multiclones
Institute of Scientific and Technical Information of China (English)
Zhang Wen-Hai; Ye Liu
2009-01-01
This paper presents a very simple method to derive the explicit transformations of the optimal economical to M phase-covariant cloning. The fidelity of clones reaches the theoretic bound [D'Ariano G M and Macchiavello C 2003 Phys. Rcv. A 67 042306]. The derived transformations cover the previous contributions [Delgado Y,Lamata L et al,2007 Phys. Rev. Lett. 98 150502] in which M must be odd.
Unbiased risk estimation method for covariance estimation
Lescornel, Hélène; Chabriac, Claudie
2011-01-01
We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.
Risk evaluation with enhaced covariance matrix
Urbanowicz, K; Richmond, P; Holyst, Janusz A.; Richmond, Peter; Urbanowicz, Krzysztof
2006-01-01
We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from diferent assets (or sources) such that each set then has similar statistical properties in terms of their probability distributions. The method is tested using historical data from both the New York and Warsaw Stock Exchanges.
Covariant quantization of the CBS superparticle
Grassi, P. A.; Policastro, G.; Porrati, M.
2001-07-01
The quantization of the Casalbuoni-Brink-Schwarz superparticle is performed in an explicitly covariant way using the antibracket formalism. Since an infinite number of ghost fields are required, within a suitable off-shell twistor-like formalism, we are able to fix the gauge of each ghost sector without modifying the physical content of the theory. The computation reveals that the antibracket cohomology contains only the physical degrees of freedom.
Torsion and geometrostasis in covariant superstrings
Energy Technology Data Exchange (ETDEWEB)
Zachos, C.
1985-01-01
The covariant action for freely propagating heterotic superstrings consists of a metric and a torsion term with a special relative strength. It is shown that the strength for which torsion flattens the underlying 10-dimensional superspace geometry is precisely that which yields free oscillators on the light cone. This is in complete analogy with the geometrostasis of two-dimensional sigma-models with Wess-Zumino interactions. 13 refs.
Linear Covariance Analysis for a Lunar Lander
Jang, Jiann-Woei; Bhatt, Sagar; Fritz, Matthew; Woffinden, David; May, Darryl; Braden, Ellen; Hannan, Michael
2017-01-01
A next-generation lunar lander Guidance, Navigation, and Control (GNC) system, which includes a state-of-the-art optical sensor suite, is proposed in a concept design cycle. The design goal is to allow the lander to softly land within the prescribed landing precision. The achievement of this precision landing requirement depends on proper selection of the sensor suite. In this paper, a robust sensor selection procedure is demonstrated using a Linear Covariance (LinCov) analysis tool developed by Draper.
ANL Critical Assembly Covariance Matrix Generation
Energy Technology Data Exchange (ETDEWEB)
McKnight, Richard D. [Argonne National Lab. (ANL), Argonne, IL (United States); Grimm, Karl N. [Argonne National Lab. (ANL), Argonne, IL (United States)
2014-01-15
This report discusses the generation of a covariance matrix for selected critical assemblies that were carried out by Argonne National Laboratory (ANL) using four critical facilities-all of which are now decommissioned. The four different ANL critical facilities are: ZPR-3 located at ANL-West (now Idaho National Laboratory- INL), ZPR-6 and ZPR-9 located at ANL-East (Illinois) and ZPPr located at ANL-West.
Covariant Calculus for Effective String Theories
Dass, N. D. Hari; Matlock, Peter
2007-01-01
A covariant calculus for the construction of effective string theories is developed. Effective string theory, describing quantum string-like excitations in arbitrary dimension, has in the past been constructed using the principles of conformal field theory, but not in a systematic way. Using the freedom of choice of field definition, a particular field definition is made in a systematic way to allow an explicit construction of effective string theories with manifest exact conformal symmetry. ...
Covariates of Craving in Actively Drinking Alcoholics
Chakravorty, Subhajit; Kuna, Samuel T.; Zaharakis, Nikola; O’Brien, Charles P.; Kampman, Kyle M.; Oslin, David
2010-01-01
The goal of this cross-sectional study was to assess the relationship of alcohol craving with biopsychosocial and addiction factors that are clinically pertinent to alcoholism treatment. Alcohol craving was assessed in 315 treatment-seeking, alcohol dependent subjects using the PACS questionnaire. Standard validated questionnaires were used to evaluate a variety of biological, addiction, psychological, psychiatric, and social factors. Individual covariates of craving included age, race, probl...
On the Problem of Permissible Covariance and Variogram Models
Christakos, George
1984-02-01
The covariance and variogram models (ordinary or generalized) are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems. For example, the efficacy of kriging, a method for interpolating, filtering, or averaging spatial phenomena, depends, to a large extent, on the covariance or variogram model chosen. The aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem, and is not included among the known covariance or variogram models, is permissible as such a model. This is done by investigating the properties of the candidate model in both the space and frequency domains. In the present article this investigation covers stationary random functions as well as intrinsic random functions (i.e., nonstationary functions for which increments of some order are stationary). Then, based on the theoretical results obtained, a procedure is outlined and successfully applied to a number of candidate models. In order to give to this procedure a more practical context, we employ "stereological" equations that essentially transfer the investigations to one-dimensional space, together with approximations in terms of polygonal functions and Fourier-Bessel series expansions. There are many benefits and applications of such a procedure. Polygonal models can be fit arbitrarily closely to the data. Also, the approximation of a particular model in the frequency domain by a Fourier-Bessel series expansion can be very effective. This is shown by theory and by example.
How covariant is the galaxy luminosity function?
Smith, Robert E
2012-01-01
We investigate the error properties of certain galaxy luminosity function (GLF) estimators. Using a cluster expansion of the density field, we show how, for both volume and flux limited samples, the GLF estimates are covariant. The covariance matrix can be decomposed into three pieces: a diagonal term arising from Poisson noise; a sample variance term arising from large-scale structure in the survey volume; an occupancy covariance term arising due to galaxies of different luminosities inhabiting the same cluster. To evaluate the theory one needs: the mass function and bias of clusters, and the conditional luminosity function (CLF). We use a semi-analytic model (SAM) galaxy catalogue from the Millennium run N-body simulation and the CLF of Yang et al. (2003) to explore these effects. The GLF estimates from the SAM and the CLF qualitatively reproduce results from the 2dFGRS. We also measure the luminosity dependence of clustering in the SAM and find reasonable agreement with 2dFGRS results for bright galaxies. ...
Autism-specific covariation in perceptual performances: "g" or "p" factor?
Directory of Open Access Journals (Sweden)
Andrée-Anne S Meilleur
Full Text Available BACKGROUND: Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination and mid-level (e.g., pattern matching tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals. METHODS: We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ and Raven Progressive Matrices (RPM. We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence. RESULTS: In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism. CONCLUSIONS: Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or "g" factor. Instead, this residual covariation is accounted for by a common perceptual process (or "p" factor, which may