Partially massless fields during inflation

Science.gov (United States)

Baumann, Daniel; Goon, Garrett; Lee, Hayden; Pimentel, Guilherme L.

2018-04-01

The representation theory of de Sitter space allows for a category of partially massless particles which have no flat space analog, but could have existed during inflation. We study the couplings of these exotic particles to inflationary perturbations and determine the resulting signatures in cosmological correlators. When inflationary perturbations interact through the exchange of these fields, their correlation functions inherit scalings that cannot be mimicked by extra massive fields. We discuss in detail the squeezed limit of the tensor-scalar-scalar bispectrum, and show that certain partially massless fields can violate the tensor consistency relation of single-field inflation. We also consider the collapsed limit of the scalar trispectrum, and find that the exchange of partially massless fields enhances its magnitude, while giving no contribution to the scalar bispectrum. These characteristic signatures provide clean detection channels for partially massless fields during inflation.

On Born approximation in black hole scattering

Science.gov (United States)

Batic, D.; Kelkar, N. G.; Nowakowski, M.

2011-12-01

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

Muonic-hydrogen molecular bound states, quasibound states, and resonances in the Born-Oppenheimer approximation

International Nuclear Information System (INIS)

Jackson, J.D.

1994-01-01

The Born-Oppenheimer approximation is used as an exploratory tool to study bound states, quasibound states, and scattering resonances in muon (μ)--hydrogen (x)--hydrogen (y) molecular ions. Our purpose is to comment on the existence and nature of the narrow states reported in three-body calculations, for L=0 and 1, at approximately 55 eV above threshold and the family of states in the same partial waves reported about 1.9 keV above threshold. We first discuss the motivation for study of excited states beyond the well-known and well-studied bound states. Then we reproduce the energies and other properties of these well-known states to show that, despite the relatively large muon mass, the Born-Oppenheimer approximation gives a good, semiquantitative description containing all the essential physics. Born-Oppenheimer calculations of the s- and p-wave scattering of d-(dμ), d-(tμ), and t-(tμ) are compared with the accurate three-body results, again with general success. The places of disagreement are understood in terms of the differences in location of slightly bound (or unbound) states in the Born-Oppenheimer approximation compared to the accurate three-body calculations

Application of the N-quantum approximation method to bound state problems

International Nuclear Information System (INIS)

Raychaudhuri, A.

1977-01-01

The N-quantum approximation (NQA) method is examined in the light of its application to bound state problems. Bound state wave functions are obtained as expansion coefficients in a truncated Haag expansion. From the equations of motion for the Heisenberg field and the NQA expansion, an equation satisfied by the wave function is derived. Two different bound state systems are considered. In one case, the bound state problem of two identical scalars by scalar exchange is analyzed using the NQA. An integral equation satisfied by the wave function is derived. In the nonrelativistic limit, the equation is shown to reduce to the Schroedinger equation. The equation is solved numerically, and the results compared with those obtained for this system by other methods. The NQA method is also applied to the bound state of two spin 1/2 particles with electromagnetic interaction. The integral equation for the wave function is shown to agree with the corresponding Bethe Salpeter equation in the nonrelativistic limit. Using the Dirac (4 x 4) matrices the wave function is expanded in terms of structure functions and the equation for the wave function is reduced to two disjoint sets of coupled equation for the structure functions

Free-Space Optical Communications: Capacity Bounds, Approximations, and a New Sphere-Packing Perspective

KAUST Repository

Chaaban, Anas

2016-02-03

The capacity of the free-space optical channel is studied. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed. This approach leads to new capacity upper bounds for a channel with a peak intensity constraint or an average intensity constraint. Under an average constraint only, the derived bound is tighter than an existing sphere-packing bound derived earlier by Farid and Hranilovic. The achievable rate of a truncated-Gaussian input distribution is also derived. It is shown that under both average and peak constraints, this achievable rate and the sphere-packing bounds are within a small gap at high SNR, leading to a simple high-SNR capacity approximation. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions.

Free-Space Optical Communications: Capacity Bounds, Approximations, and a New Sphere-Packing Perspective

KAUST Repository

Chaaban, Anas; Morvan, Jean-Marie; Alouini, Mohamed-Slim

2016-01-01

The capacity of the free-space optical channel is studied. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed. This approach leads to new capacity upper bounds for a channel with a peak intensity constraint or an average intensity constraint. Under an average constraint only, the derived bound is tighter than an existing sphere-packing bound derived earlier by Farid and Hranilovic. The achievable rate of a truncated-Gaussian input distribution is also derived. It is shown that under both average and peak constraints, this achievable rate and the sphere-packing bounds are within a small gap at high SNR, leading to a simple high-SNR capacity approximation. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions.

Could a Weak Coupling Massless SU(5) Theory Underly the Standard Model S-Matrix

Science.gov (United States)

White, Alan R.

2011-04-01

The unitary Critical Pomeron connects to a unique massless left-handed SU(5) theory that, remarkably, might provide an unconventional underlying unification for the Standard Model. Multi-regge theory suggests the existence of a bound-state high-energy S-Matrix that replicates Standard Model states and interactions via massless fermion anomaly dynamics. Configurations of anomalous wee gauge boson reggeons play a vacuum-like role. All particles, including neutrinos, are bound-states with dynamical masses (there is no Higgs field) that are formed (in part) by anomaly poles. The contributing zero-momentum chirality transitions break the SU(5) symmetry to vector SU(3)⊗U(1) in the S-Matrix. The high-energy interactions are vector reggeon exchanges accompanied by wee boson sums (odd-signature for the strong interaction and even-signature for the electroweak interaction) that strongly enhance couplings. The very small SU(5) coupling, αQUD ≲ 1/120, should be reflected in small (Majorana) neutrino masses. A color sextet quark sector, still to be discovered, produces both Dark Matter and Electroweak Symmetry Breaking. Anomaly color factors imply this sector could be produced at the LHC with large cross-sections, and would be definitively identified in double pomeron processes.

Partially massless higher-spin theory

Energy Technology Data Exchange (ETDEWEB)

Brust, Christopher [Perimeter Institute for Theoretical Physics,31 Caroline St. N, Waterloo, Ontario N2L 2Y5 (Canada); Hinterbichler, Kurt [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH 44106 (United States)

2017-02-16

We study a generalization of the D-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that includes “third-order” Killing tensors. Gauging this algebra with the Vasiliev formalism leads to a fully non-linear theory which is expected to be UV complete, includes gravity, and can live on dS as well as AdS. The linearized spectrum includes three massive particles and an infinite tower of partially massless particles, in addition to the usual spectrum of particles present in the Vasiliev theory, in agreement with predictions from a putative dual CFT with the same symmetry algebra. We compute the masses of the particles which are not fixed by the massless or partially massless gauge symmetry, finding precise agreement with the CFT predictions. This involves computing several dozen of the lowest-lying terms in the expansion of the trilinear form of the enlarged higher-spin algebra. We also discuss nuances in the theory that occur in specific dimensions; in particular, the theory dramatically truncates in bulk dimensions D=3,5 and has non-diagonalizable mixings which occur in D=4,7.

Partially massless higher-spin theory

International Nuclear Information System (INIS)

Brust, Christopher; Hinterbichler, Kurt

2017-01-01

We study a generalization of the D-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that includes “third-order” Killing tensors. Gauging this algebra with the Vasiliev formalism leads to a fully non-linear theory which is expected to be UV complete, includes gravity, and can live on dS as well as AdS. The linearized spectrum includes three massive particles and an infinite tower of partially massless particles, in addition to the usual spectrum of particles present in the Vasiliev theory, in agreement with predictions from a putative dual CFT with the same symmetry algebra. We compute the masses of the particles which are not fixed by the massless or partially massless gauge symmetry, finding precise agreement with the CFT predictions. This involves computing several dozen of the lowest-lying terms in the expansion of the trilinear form of the enlarged higher-spin algebra. We also discuss nuances in the theory that occur in specific dimensions; in particular, the theory dramatically truncates in bulk dimensions D=3,5 and has non-diagonalizable mixings which occur in D=4,7.

Cosmological stability bound in massive gravity and bigravity

International Nuclear Information System (INIS)

Fasiello, Matteo; Tolley, Andrew J.

2013-01-01

We give a simple derivation of a cosmological bound on the graviton mass for spatially flat FRW solutions in massive gravity with an FRW reference metric and for bigravity theories. This bound comes from the requirement that the kinetic term of the helicity zero mode of the graviton is positive definite. The bound is dependent only on the parameters in the massive gravity potential and the Hubble expansion rate for the two metrics. We derive the decoupling limit of bigravity and FRW massive gravity, and use this to give an independent derivation of the cosmological bound. We recover our previous results that the tension between satisfying the Friedmann equation and the cosmological bound is sufficient to rule out all observationally relevant FRW solutions for massive gravity with an FRW reference metric. In contrast, in bigravity this tension is resolved due to different nature of the Vainshtein mechanism. We find that in bigravity theories there exists an FRW solution with late-time self-acceleration for which the kinetic terms for the helicity-2, helicity-1 and helicity-0 are generically nonzero and positive making this a compelling candidate for a model of cosmic acceleration. We confirm that the generalized bound is saturated for the candidate partially massless (bi)gravity theories but the existence of helicity-1/helicity-0 interactions implies the absence of the conjectured partially massless symmetry for both massive gravity and bigravity

Massive and massless gauge fields of any spin and symmetry

International Nuclear Information System (INIS)

Hussain, F.; Jarvis, P.D.

1988-05-01

An analysis of the BRST approach to massive and massless gauge fields of any spin and symmetry is presented. Previous results on massless gauge fields are extended to totally antisymmetric massless tensors and Kaehler-Dirac particles. Two methods for arriving at a BRST invariant, massive theory from the corresponding massless one are discussed. The first allows for an interpretation in terms of dimensional reduction, while the second keeps the BRST operator of the massless theory, but employs gauge invariant fields. (author). 10 refs

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

Science.gov (United States)

Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang

2016-01-01

Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.

New approximation to the bound states of Schroedinger operators with coulomb interaction

International Nuclear Information System (INIS)

Nunez, M.A.; Izquierdo B., G.

1994-01-01

In this work, the authors present a mathematical formulation of the physical fact that the bound states of a quantum system confined into a box Ω (with impenetrable walls) are similar to those of the unconfined system, if the box Ω is sufficiently large, and it is shown how the bound states of atomic and molecular Hamiltonians can be approximated by those of the system confined for a box Ω large enough (Dirichlet eigenproblem in Ω). Thus, a method for computing bound states is obtained which has the advantage of reducing the problem to the case of compact operators. This implies that a broad class of numerical and analytic techniques used for solving the Dirichlet problem, may be applied in full strength to obtain accurate computations of energy levels, wave functions, and other physical properties of interest

Quasiparadoxes of massless QED

International Nuclear Information System (INIS)

Smilga, A.V.

1990-04-01

We show that the limit m e =0 in the conventional QED is not smooth. In contrast to the massless QED the massive QED, however small the mass is, involves finite probability chirality breaking processes. The chirality breaking effects may be observed provided the size of experimental installation is greater than the formation length ∼ E/m 2 . We discuss also the finite cross sections of virtual longitudinal photon production and scattering in massless QED recently found by Gorsky, Ioffe and Khodjamirian and argue that real longitudinal photons do not interact while the limit of zero virtuality is not smooth. (author). 23 refs, 4 figs

On bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables.

Science.gov (United States)

Hung, Tran Loc; Giang, Le Truong

2016-01-01

Using the Stein-Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.

Charged boson bound states in the kerr-newman metric

International Nuclear Information System (INIS)

Li Yuanjie; Zhang Duanming

1986-01-01

Charged boson bound states in Kerr-Newman metric are discussed. It is found that massless boson cannot be attracted by Kerr-Newman black hole to form bound states. For the massive boson, the condition of the nonbound states when 0 2 - Q 2 and both the condition and wave functions of the bound states when a = √M 2 - Q 2 are obtained. The energy mode of the bound states is single, E = (m√M 2 - Q 2 + eQM)/(2M 2 - Q 2 ). When Q = 0 or e = 0, the conclusion is in agreement with that of Zhang Shiwei and Su Rukeng

Frames of exponentials:lower frame bounds for finite subfamilies, and approximation of the inverse frame operator

DEFF Research Database (Denmark)

Christensen, Ole; Lindner, Alexander M

2001-01-01

We give lower frame bounds for finite subfamilies of a frame of exponentials {e(i lambdak(.))}k is an element ofZ in L-2(-pi,pi). We also present a method for approximation of the inverse frame operator corresponding to {e(i lambdak(.))}k is an element ofZ, where knowledge of the frame bounds for...

Ground states of the massless Derezinski-Gerard model

International Nuclear Information System (INIS)

Ohkubo, Atsushi

2009-01-01

We consider the massless Derezinski-Gerard model introduced by Derezinski and Gerard in 1999. We give a sufficient condition for the existence of a ground state of the massless Derezinski-Gerard model without the assumption that the Hamiltonian of particles has compact resolvent.

Upper bound on the radii of black-hole photonspheres

International Nuclear Information System (INIS)

Hod, Shahar

2013-01-01

One of the most remarkable predictions of the general theory of relativity is the existence of black-hole “photonspheres”, compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by r γ ⩽3M, where M is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound

Stochastic massless fields I: Integer spin

International Nuclear Information System (INIS)

Lim, S.C.

1981-04-01

Nelson's stochastic quantization scheme is applied to classical massless tensor potential in ''Coulomb'' gauge. The relationship between stochastic potential field in various gauges is discussed using the case of vector potential as an illustration. It is possible to identify the Euclidean tensor potential with the corresponding stochastic field in physical Minkowski space-time. Stochastic quantization of massless fields can also be carried out in terms of field strength tensors. An example of linearized stochastic gravitational field in vacuum is given. (author)

A material optimization model to approximate energy bounds for cellular materials under multiload conditions

DEFF Research Database (Denmark)

Guedes, J.M.; Rodrigues, H.C.; Bendsøe, Martin P.

2003-01-01

This paper describes a computational model, based on inverse homogenization and topology design, for approximating energy bounds for two-phase composites under multiple load cases. The approach allows for the identification of possible single-scale cellular materials that give rise to the optimal...

On bound states of photons in noncommutative U(1) gauge theory

International Nuclear Information System (INIS)

Fatollahi, A.H.; Jafari, A.

2006-01-01

We consider the possibility that photons of noncommutative U(1) gauge theory can make bound states. Using the potential model, developed based on the constituent gluon picture of QCD glue-balls, arguments are presented in favor of the existence of these bound states. The basic ingredient of the potential model is that the self-interacting massless gauge particles may get mass by the inclusion of non-perturbative effects. (orig.)

Massless representations and admissibility condition for higher spin superalgebras

Energy Technology Data Exchange (ETDEWEB)

Konstein, S E; Vasiliev, M A

1989-01-16

Massless particle representations of various infinite-dimensional higher spin superalgebras proposed previously are constructed. We analyse which of higher spin superalgebras obey the requirement (the admissibility condition) of possessing massless unitary representations with the same spectra of spins as predicted by the structure of gauge fields originating from these superalgebras. It is argued that those higher spin superalgebras, which obey the admissibility condition, can serve as rigid supersymmetries in nontrivial consistent gauge theories of massless fields of all spins.

Kac--Moody current algebras of D = 2 massless gauge theories, their representations and applications

International Nuclear Information System (INIS)

Craigie, N.S.; Nahm, W.; Narain, K.S.

1987-01-01

We give a classification of the Kac--Moody current algebras of all the possible massless fermion-gauge theories in two dimensions. It is shown that only Kac--Moody algebras based on A/sub N/, B/sub N/, C/sub N/, and D/sub N/ in the Cartan classification with all possible central charge occur.The representation of local fermion fields and simply laced Kac--Moody algebras with minimal central charge in terms of free boson fields on a compactified space is discussed in detail, where stress is laid on the role played by the boundary conditions on the various collective modes. Fractional solitons and the possible soliton representation of certain nonsimply laced algebras is also analysed. We briefly discuss the relationship between the massless bound state sector of these two-dimensional gauge theories and the critically coupled two-dimensional nonlinear sigma model, which share the same current algebra. Finally we briefly discuss the relevance of Sp(n) Kac--Moody algebras to the physics of monopole-fermion systems. copyright 1987 Academic Press, Inc

Approximate Q.C.D. lower bound for the bag constant B

International Nuclear Information System (INIS)

Nielsen, H.B.

1978-01-01

Using an article by Savvidy from 1977 in which a state in Q.C.D. with lower energy than the perturbative vacuum was found, the author calculates an approximate lower bound for the M.I.T. bag constant B relative to the Q.C.D. coupling parameter Λ. With an M.I.T. bag constant Bsup(1/4)=145 MeV the author finds Λsub(P)<=0.89 GeV when the propagator of the gluon is used to renormalize the coupling constant. (Auth.)

Partially massless graviton on beyond Einstein spacetimes

Science.gov (United States)

Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael

2017-06-01

We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.

A fast algorithm for determining bounds and accurate approximate p-values of the rank product statistic for replicate experiments.

Science.gov (United States)

Heskes, Tom; Eisinga, Rob; Breitling, Rainer

2014-11-21

The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution. We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood. We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .

Twistor diagrams and massless Moeller scattering

International Nuclear Information System (INIS)

Hodges, A.P.

1983-01-01

The theory of twistor diagrams, as devised by Penrose, is intended to lead to a manifestly finite account of scattering amplitudes in quantum field theory. The theory is here extended to a more general type of interaction between massless fields than has hitherto been described. It is applied to the example of first-order massless Moeller scattering in quantum electrodynamics. It is shown that earlier studies of this example have failed to render a correct account, in particular by overlooking an infrared divergency, but that the scattering data can nevertheless be represented within the twistor formalism. (author)

Lorentz transformations, sideways shift and massless spinning particles

Science.gov (United States)

Bolonek-Lasoń, K.; Kosiński, P.; Maślanka, P.

2017-06-01

Recently (Stone et al. (2015) [16]) the influence of the so called ;Wigner translations; (more generally-Lorentz transformations) on circularly polarized Gaussian packets (providing the solution to Maxwell equations in paraxial approximation) has been studied. It appears that, within this approximation, the Wigner translations have an effect of shifting the wave packet trajectory parallel to itself by an amount proportional to the photon helicity. It has been suggested that this shift may result from specific properties of the algebra of Poincare generators for massless particles. In the present letter we describe the general relation between transformation properties of electromagnetic field on quantum and classical levels. It allows for a straightforward derivation of the helicity-dependent transformation rules. We present also an elementary derivation of the formula for sideways shift based on classical Maxwell theory. Some comments are made concerning the generalization to higher helicities and the relation to the coordinate operator defined long time ago by Pryce.

Lorentz transformations, sideways shift and massless spinning particles

Directory of Open Access Journals (Sweden)

K. Bolonek-Lasoń

2017-06-01

Full Text Available Recently (Stone et al. (2015 [16] the influence of the so called “Wigner translations” (more generally-Lorentz transformations on circularly polarized Gaussian packets (providing the solution to Maxwell equations in paraxial approximation has been studied. It appears that, within this approximation, the Wigner translations have an effect of shifting the wave packet trajectory parallel to itself by an amount proportional to the photon helicity. It has been suggested that this shift may result from specific properties of the algebra of Poincare generators for massless particles. In the present letter we describe the general relation between transformation properties of electromagnetic field on quantum and classical levels. It allows for a straightforward derivation of the helicity-dependent transformation rules. We present also an elementary derivation of the formula for sideways shift based on classical Maxwell theory. Some comments are made concerning the generalization to higher helicities and the relation to the coordinate operator defined long time ago by Pryce.

Lorentz transformations, sideways shift and massless spinning particles

Energy Technology Data Exchange (ETDEWEB)

Bolonek-Lasoń, K. [Department of Statistical Methods, Faculty of Economics and Sociology (Poland); Kosiński, P. [Department of Computer Science, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153, 90-236 Łódź (Poland); Maślanka, P., E-mail: pmaslan@uni.lodz.pl [Department of Computer Science, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153, 90-236 Łódź (Poland)

2017-06-10

Recently (Stone et al. (2015) ) the influence of the so called “Wigner translations” (more generally-Lorentz transformations) on circularly polarized Gaussian packets (providing the solution to Maxwell equations in paraxial approximation) has been studied. It appears that, within this approximation, the Wigner translations have an effect of shifting the wave packet trajectory parallel to itself by an amount proportional to the photon helicity. It has been suggested that this shift may result from specific properties of the algebra of Poincare generators for massless particles. In the present letter we describe the general relation between transformation properties of electromagnetic field on quantum and classical levels. It allows for a straightforward derivation of the helicity-dependent transformation rules. We present also an elementary derivation of the formula for sideways shift based on classical Maxwell theory. Some comments are made concerning the generalization to higher helicities and the relation to the coordinate operator defined long time ago by Pryce.

Massive and mass-less Yang-Mills and gravitational fields

NARCIS (Netherlands)

Veltman, M.J.G.; Dam, H. van

1970-01-01

Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in

Mass generation in perturbed massless integrable models

International Nuclear Information System (INIS)

Controzzi, D.; Mussardo, G.

2005-01-01

We extend form-factor perturbation theory to non-integrable deformations of massless integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory

The Weinberg-Witten theorem on massless particles: an essay

International Nuclear Information System (INIS)

Loebbert, F.

2008-01-01

In this essay we deal with the Weinberg-Witten theorem which imposes limitations on massless particles. First we motivate a classification of massless particles given by the Poincare group as the symmetry group of Minkowski spacetime. We then use the fundamental structure of the background in the form of Poincare covariance to derive restrictions on charged massless particles known as the Weinberg-Witten theorem. We address possible misunderstandings in the proof of this theorem motivated by several papers on this topic. In the last section the consequences of the theorem are discussed. We treat it in the context of known particles and as a constraint for emergent theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

Bounded-Degree Approximations of Stochastic Networks

Energy Technology Data Exchange (ETDEWEB)

Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar

2017-06-01

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

Macroscopic (and microscopic massless modes

Directory of Open Access Journals (Sweden)

Michael C. Abbott

2015-05-01

Full Text Available We study certain spinning strings exploring the flat directions of AdS3×S3×S3×S1, the massless sector cousins of su(2 and sl(2 sector spinning strings. We describe these, and their vibrational modes, using the D(2,1;α2 algebraic curve. By exploiting a discrete symmetry of this structure which reverses the direction of motion on the spheres, and alters the masses of the fermionic modes s→κ−s, we find out how to treat the massless fermions which were previously missing from this formalism. We show that folded strings behave as a special case of circular strings, in a sense which includes their mode frequencies, and we are able to recover this fact in the worldsheet formalism. We use these frequencies to calculate one-loop corrections to the energy, with a version of the Beisert–Tseytlin resummation.

Relativistic bound state approach to fundamental forces including gravitation

Directory of Open Access Journals (Sweden)

Morsch H.P.

2012-06-01

Full Text Available To describe the structure of particle bound states of nature, a relativistic bound state formalism is presented, which requires a Lagrangian including scalar coupling of two boson fields. The underlying mechanisms are quite complex and require an interplay of overlapping boson fields and fermion-antifermion production. This gives rise to two potentials, a boson-exchange potential and one identified with the long sought confinement potential in hadrons. With minimal requirements, two elementary massless fermions (quantons - with and without charge - and one gauge boson, hadrons and leptons but also atoms and gravitational systems are described by bound states with electric and magnetic coupling between the charges and spins of quantons. No need is found for colour, Higgs-coupling and supersymmetry.

The trace anomaly and massless scalar degrees of freedom

Energy Technology Data Exchange (ETDEWEB)

Gianotti, Maurizio [Los Alamos National Laboratory; Mottola, Emil [Los Alamos National Laboratory

2008-01-01

The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, {open_square}T{sup {mu}{nu}}J{sup {alpha}}J{sup {beta}}, and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass m{yields}0. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this amplitude and the existence of the massless scalar pole is determined completely by its ultraviolet finite terms, together with the requirements of Poincare invariance of the vacuum, Bose symmetry under interchange of J{sup {alpha}} and J{sup {beta}}, and vector current and stress-tensor conservation. We derive a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to {delta}(k{sup 2}) and therefore contains a massless scalar intermediate state in the conformal limit of zero electron mass. The effective action corresponding to the trace of the triangle amplitude can be expressed in local form by the introduction of two scalar auxiliary fields which satisfy massless wave equations. These massless scalar degrees of freedom couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects.

Conservation of lepton charges, massive majorana and massless neutrinos

International Nuclear Information System (INIS)

Petcov, S.T.; Toshev, S.T.

1984-01-01

It is shown that the necessary and sufficient condition for the presence of k massless and (n-k) massive nondegenerate Majorana neutrinos in a theory with n neutrino flavours and a neutrino mass term of Majorana type is the existence of k standard and no other conserved lepton charges. Two-loop Majorana mass corrections for neutrinos, massless at tree level, are also briefly discussed. (orig.)

Hunting Down Massless Dark Photons in Kaon Physics

Science.gov (United States)

Fabbrichesi, M.; Gabrielli, E.; Mele, B.

2017-07-01

If dark photons are massless, they couple to standard-model particles only via higher dimensional operators, while direct (renormalizable) interactions induced by kinetic mixing, which motivates most of the current experimental searches, are absent. We consider the effect of possible flavor-changing magnetic-dipole couplings of massless dark photons in kaon physics. In particular, we study the branching ratio for the process K+→π+π0γ ¯ with a simplified-model approach, assuming the chiral quark model to evaluate the hadronic matrix element. Possible effects in the K0-K¯ 0 mixing are taken into account. We find that branching ratios up to O (10-7) are allowed—depending on the dark-sector masses and couplings. Such large branching ratios for K+→π+π0γ ¯ could be of interest for experiments dedicated to rare K+ decays like NA62 at CERN, where γ ¯ can be detected as a massless invisible system.

Quantum Prisoners' Dilemma in Fluctuating Massless Scalar Field

Science.gov (United States)

Huang, Zhiming

2017-12-01

Quantum systems are easily affected by external environment. In this paper, we investigate the influences of external massless scalar field to quantum Prisoners' Dilemma (QPD) game. We firstly derive the master equation that describes the system evolution with initial maximally entangled state. Then, we discuss the effects of a fluctuating massless scalar field on the game's properties such as payoff, Nash equilibrium, and symmetry. We find that for different game strategies, vacuum fluctuation has different effects on payoff. Nash equilibrium is broken but the symmetry of the game is not violated.

Bootstrap bound for conformal multi-flavor QCD on lattice

Energy Technology Data Exchange (ETDEWEB)

Nakayama, Yu [Department of Physics, Rikkyo University,Toshima, Tokyo 171-8501 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo,5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583 (Japan)

2016-07-08

The recent work by Iha et al. shows an upper bound on mass anomalous dimension γ{sub m} of multi-flavor massless QCD at the renormalization group fixed point from the conformal bootstrap in SU(N{sub F}){sub V} symmetric conformal field theories under the assumption that the fixed point is realizable with the lattice regularization based on staggered fermions. We show that the almost identical but slightly stronger bound applies to the regularization based on Wilson fermions (or domain wall fermions) by studying the conformal bootstrap in SU(N{sub f}){sub L}×SU(N{sub f}){sub R} symmetric conformal field theories. For N{sub f}=8, our bound implies γ{sub m}<1.31 to avoid dangerously irrelevant operators that are not compatible with the lattice symmetry.

Four loop massless propagators: An algebraic evaluation of all master integrals

International Nuclear Information System (INIS)

Baikov, P.A.; Chetyrkin, K.G.

2010-01-01

The old 'glue-and-cut' symmetry of massless propagators, first established in Ref. (Chetyrkin and Tkachov, 1981), leads -after reduction to master integrals is performed - to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (ζ 2n ) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.

On massless representations of the Q-deformed Poincare algebra

International Nuclear Information System (INIS)

Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.

1993-01-01

This talk is devoted to the construction of massless representations of the q-deformed Poincare algebra. In section 2 we give Hilbert space representations of the SL q (2, C)-covariant quantum space. We then show in the next section how the generators of the q-Poincare algebra can be expressed in terms of operators which live in the light cone. The q-deformed massless one-particle states are considered in section 4. (orig.)

Massless Interacting Scalar Fields in de Sitter space

CERN Document Server

López Nacir, Diana

2016-10-28

We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\\sqrt\\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\\sqrt\\lambda$ and in $1/N$.

Massless gluino and pseudoscalar meson family

International Nuclear Information System (INIS)

Smilga, A.V.; Vysotskij, M.I.

1982-01-01

It is shown that masslessness of the glUino leads necessarily to the existence of the light isosinglet pseudoscalar boson not observed in experiment. Thus, any realistic supersymmetry model must include the mechanism for generating the gluino mass

Time-dependent massless Dirac fermions in graphene

Energy Technology Data Exchange (ETDEWEB)

Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)

2015-10-30

Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.

''Massless'' vector field in de Sitter universe

International Nuclear Information System (INIS)

Garidi, T.; Gazeau, J.-P.; Rouhani, S.; Takook, M. V.

2008-01-01

We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al., ibid. 43, 6379 (2002).] The term ''massless'' is used by reference to conformal invariance and propagation on the dS lightcone whereas ''massive'' refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta-Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function

``Massless'' vector field in de Sitter universe

Science.gov (United States)

Garidi, T.; Gazeau, J.-P.; Rouhani, S.; Takook, M. V.

2008-03-01

We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al., ibid. 43, 6379 (2002).] The term ``massless'' is used by reference to conformal invariance and propagation on the dS lightcone whereas ``massive'' refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta-Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function.

Symanzik approach in modeling of bound states of Dirac particle in singular background

Directory of Open Access Journals (Sweden)

Pismak Yu. M.

2017-01-01

Full Text Available In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are studied. For localized near plane Dirac particle the expression for current, charge and density are presented. For bound state with massless dispersion law the current, charge and density are calculated for simplified model with 2 parameter exactly.The model can find application to a wide class of phenomena arising by the interaction of fields of quantum electrodynamics with two-dimensional materials.

Four loop massless propagators: An algebraic evaluation of all master integrals

Energy Technology Data Exchange (ETDEWEB)

Baikov, P.A., E-mail: baikov@theory.sinp.msu.r [Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation); Chetyrkin, K.G., E-mail: konstantin.chetyrkin@kit.ed [Institut fuer Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe (Germany)] [Institute for Nuclear Research, Russian Academy of Sciences, Moscow 117312 (Russian Federation)

2010-10-01

The old 'glue-and-cut' symmetry of massless propagators, first established in Ref. (Chetyrkin and Tkachov, 1981), leads -after reduction to master integrals is performed - to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas ({zeta}{sub 2n}) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.

New non-linear modified massless Klein-Gordon equation

Energy Technology Data Exchange (ETDEWEB)

Asenjo, Felipe A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Facultad de Ingenieria y Ciencias, Santiago (Chile); Hojman, Sergio A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Santiago (Chile); Universidad de Chile, Departamento de Fisica, Facultad de Ciencias, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2017-11-15

The massless Klein-Gordon equation on arbitrary curved backgrounds allows for solutions which develop ''tails'' inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential. (orig.)

Massless fermions and Kaluza--Klein theory with torsion

International Nuclear Information System (INIS)

Wu, Y.; Zee, A.

1984-01-01

A pure Kaluza--Klein theory contains no massless fermion in four-dimensional theory. We investigate the effect of introducing torsion on the internal manifold and find that there are massless fermions. The hope is that given an isometry group the representation to which these fermions belong is fixed, in contrast to the situation in Yang--Mills theory. We show that this is indeed the case, but the representations do not appear to be the ones favored by current theoretical prejudice. The cases with parallelizable torsions on a group manifold as the internal manifold are analyzed in detail

Massive and massless supersymmetry: Multiplet structure and unitary irreducible representations

International Nuclear Information System (INIS)

Jarvis, P.D.

1976-01-01

UIR's of the supersymmetry algebra for the massive and massless cases are analyzed covariantly (without the use of induced representations) in terms of their component spins. For the massive case normalized basis vectors vertical-barp 2 >0, j 0 ; sigma; pjlambda> are constructed, where j 0 is the ''superspin'' and sigma is an additional quantum number serving to distinguish the different vertical-barpjlambda>, the constituent p 2 >0, spin-j UIR's of the Poincare group. For the massless case, normalized basis vectors vertical-barp 2 =0, lambda 0 ; plambda> are similarly constructed, where lambda 0 is the ''superhelicity.'' Matrix elements of the supersymmetry generators, in these bases, are explicitly given. The ''sigma basis'' is used to define weight diagrams for the massive UIR's of supersymmetry, and their properties are briefly described. Eigenfunctions ω/sub sigma/(theta) are also defined, and their connection with the reduction of higher spin massive superfields PHI/subJ/(x,theta) is discussed. Finally, it is shown how gauge dependence necessarily arises with certain massless superfields. The massless scalar superfield, both gauge-dependent and gauge-independent, is discussed as an example

The transient M/G/1/0 queue: some bounds and approximations for light traffic with application to reliability

Directory of Open Access Journals (Sweden)

J. Ben Atkinson

1995-01-01

Full Text Available We consider the transient analysis of the M/G/1/0 queue, for which Pn(t denotes the probability that there are no customers in the system at time t, given that there are n(n=0,1 customers in the system at time 0. The analysis, which is based upon coupling theory, leads to simple bounds on Pn(t for the M/G/1/0 and M/PH/1/0 queues and improved bounds for the special case M/Er/1/0. Numerical results are presented for various values of the mean arrival rate λ to demonstrate the increasing accuracy of approximations based upon the above bounds in light traffic, i.e., as λ→0. An important area of application for the M/G/1/0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have λ values that are small relative to the mean service rate, the approximations are potentially useful in that context. A duality relation between the M/G/1/0 and GI/M/1/0 queues is also described.

Models for light QCD bound states

International Nuclear Information System (INIS)

LaCourse, D.P.

1992-01-01

After a brief overview of Regge, tower, and heavy-quark experimental data, this thesis examines two massless wave equations relevant to quark bound states. We establish general conditions on the Lorentz scalar and Lorentz vector potentials which yield arbitrary leading Regge trajectories for the case of circular classical motion. A semi-classical approximation which includes radial motion reproduces remarkably well the exact solutions. Conditions for tower structure are examined, and found to be incompatible with conditions which give a Nambu stringlike Regge slope. The author then proposes a generalization of the usual potential model of quark bound states in which the confining flux tube is a dynamical object carrying both angular momentum and energy. The Q bar Q-string system with spinless quarks is quantized using an implicit operator technique and the resulting relativistic wave equation is solved. For heavy quarks the usual Schroedinger valence-quark model is recovered. The Regge slope with light quarks agree with the classical rotating-string result and is significantly larger and the effects of short-range forces are also considered. A relativistic generalization of the quantized flux tube model predicts the glueball ground state mass to be √3/α' ≅ 1.9 GeV where α' is the normal Regge slope. The groundstate as well as excited levels like considerably above the expectations of previous models and also above various proposed experimental candidates. The glueball Regge slope is only about three-eighths that for valence quark hadrons. A semi-classical calculation of the Regge slope is in good agreement with a numerically exact value

Can massless neutrinos dominate the universe

International Nuclear Information System (INIS)

Kolb, E.W.

1980-01-01

The restrictions from cosmological considerations on masses and lifetimes of neutral, weakly interacting fermions are reviewed. In particular, the possibility that the massless decay products of a heavy neutrino dominate the energy density of the present universe is discussed in detail. 4 figures

Inertia effects on the rigid displacement approximation of tokamak plasma vertical motion

International Nuclear Information System (INIS)

Carrera, R.; Khayrutdinov, R.R.; Azizov, E.A.; Montalvo, E.; Dong, J.Q.

1991-01-01

Elongated plasmas in tokamaks are unstable to axisymmetric vertical displacements. The vacuum vessel and passive conductors can stabilize the plasma motion in the short time scale. For stabilization of the plasma movement in the long time scale an active feedback control system is required. A widely used method of plasma stability analysis uses the Rigid Displacement Model (RDM) of plasma behavior. In the RDM it is assumed that the plasma displacement is small and usually plasma inertia effects are neglected. In addition, it is considered that no changes in plasma shape, plasma current, and plasma current profile take place throughout the plasma motion. It has been demonstrated that the massless-filament approximation (instantaneous force-balance) accurately reproduces the unstable root of the passive stabilization problem. Then, on the basis that the instantaneous force-balance approximation is correct in the passive stabilization analysis, the massless approximation is utilized also in the study of the plasma vertical stabilization by active feedback. The authors show here that the RDM (without mass effects included) does not provide correct stability results for a tokamak configuration (plasma column, passive conductors, and feedback control coils). Therefore, it is concluded that inertia effects have to be retained in the RDM system of equations. It is shown analytically and numerically that stability diagrams with and without plasma-mass corrections differ significantly. When inertia effects are included, the stability region is more restricted than obtained in the massless approximation

Limit on possible energy-dependent velocities for massless particles

International Nuclear Information System (INIS)

Haines, T.J.; Alexandreas, D.E.; Allen, R.C.; Biller, S.; Berley, D.; Burman, R.L.; Cady, D.R.; Chang, C.Y.; Dingus, B.L.; Dion, G.M.; Ellsworth, R.W.; Goodman, J.A.; Hoffman, C.M.; Lloyd-Evans, J.; Nagle, D.E.; Potter, M.; Sandberg, V.D.; Wilkinson, C.A.; Yodh, G.B.

1990-01-01

A basic tenet of special relativity is that all massless particles travel at a constant, energy-independent velocity. Astrophysical data, including observation of the Crab pulsar at ∼100 MeV and the recent detection of the pulsar in Hercules X-1 at energies ≥100 TeV, are used to place new experimental constraints on energy-dependent deviations from constant velocity for massless particles. Previous experiments reached energies ∼10 GeV; this analysis improves the previous constraints by 7 orders of magnitude

On the Pomeranchuk singularity in massless vector theories

International Nuclear Information System (INIS)

Bartels, J.; Hamburg Univ.

1980-06-01

It is shown that the Pomeron in massless (abelian of nonabelian) vector theories, as derived from a perturbative high energy description which satisfies unitarity, comes as a diffusion problem in the logarithmic scale of transverse momentum. For a realistic theory there are reasons to expect that this diffusion should come to a stop: (a) the long range forces of the massless gluons should be screened, (b) the Pomeranchuk singularity in the j-plane should be t-dependant, and (c) there should not be a discontinuity in the zero mass limit at t = 0 or in the t 0 limit of the massless case. In the third part we outline a scheme for summing all diagrams which are required by unitarity. It uses reggeon field theory in zero transverse dimensions and leads to: (i) the diffusion comes to a stop (zero drift and zero diffusion constant); (ii) the total cross section is constant (up to powers of lns); (iii) in order to give a meaning to the divergent perturbation expansion, one has to add a nonperturbative term of the order exp(-const/g 2 ). (orig.)

On a manifestation of the anomalies in the massless QED

International Nuclear Information System (INIS)

Gorskij, A.S.

1989-01-01

The questions concerned with the axial and conformal anomalies in the massless QED are discussed. It is shown that the interaction of the longitudinal real photons is proportional to the β function of the theory and the corresponding matrix element L |Θ αβ |γ L > where Θ αβ is energy-momentum tensor has a common features with the nonvanishing matrix element α |γ> in the massless limit. 7 refs.; 2 figs

Massless radioactivity: a medical must?

International Nuclear Information System (INIS)

Wolterbeek, H.Th

2013-01-01

Full text: The authoritative body in the field of nomenclature for radiochemistry is the International Union of Pure and Applied Chemistry (IUPAC). The concepts of specific activity, radioactivity concentration, carrier, carrier-free, and no-carrier-added have been) and are also recently discussed as to their correctness, relevance, clarity and consistency. Here, specific activity (sa) is suggested as to be defined as the activity (a) of a specified radioisotope in an amount of substance divided by the mass (m) of the total number of atoms (sa=a/m). Qaim, in a recent review of the future of medical radionuclides, justly argues that both yield, radionuclide purity and specific activity should be increased: here, again, however, the term specific activity deserves attention. What should be the goal in increasing specific activity? Up to as near as possible to massless? Approaching massless in terms of the smallest achievable m value? Taking the radionuclide n X, in physics specific activity is defined as both activity and mass related to n X, in radiochemistry specific activity is defined as the activity of n X related to the mass of all X, but in nuclear medicine most interest is in what IUPAC calls activity concentration, that is, the activity of n X in relation to the mass or volume of the material in which n X is present. This means that, apparently, nuclear medicine asks for high activity concentration of n X in non-isotopic carriers. Does this always imply the highest possible n X specific activity? The presentation focuses on this issue: examples are given that show both the absence of any need for the highest possible specific activity (e.g. 99 Mo, 166 Ho) and the need for 'as-near-as-possible to massless' (e.g. 99m Tc, 177 Lu, α-particles), in all cases in dependence of the radionuclide's position in the production chain and its eventual application in nuclear diagnostics or - therapy

Scale transformation and massless limit in neutral-vector field theory. [Gauge transformation unified theory

Energy Technology Data Exchange (ETDEWEB)

Kubo, R; Takahashi, Y; Yokoyama, K

1975-01-01

In a wide class of neutral vector field theories, in which massive and massless fields are described in a unified way and a unique massless limit exists to quantum electrodynamics in covariant gauges, the commutability of the scale transformation and the massless limit is examined. It is shown that there occurs no anomaly with respect to the assignment for scale dimensions of relevant fields. Connection of scale transformation and gauge transformation is also discussed.

Free massless scalar fields in two dimensions

International Nuclear Information System (INIS)

Hadjiivanov, L.K.

1980-01-01

A common Fock space for two free massless scalar fields, nonlocal with respect to each other, is constructed. The operators corresponding to the two formal charges are correctly defined and it is shown that they generate translationally invariant states from the vacuum

Hydrodynamical model with massless constituents

International Nuclear Information System (INIS)

Chiu, C.B.; Wang, K.H.

1974-01-01

Within the constituent hydrodynamical model, it is shown that the total number of constituents is conserved, if these constituents are massless and satisfy the Fermi-Dirac distribution. A simple scheme for the transition from the constituent-phase to the hadron-phase is suggested, and the hadron inclusive momentum spectra are presented for this case. This phase transition scheme predicts the average transverse momentum of meson resonances which is compatible with the data. (U.S.)

Quasinormal modes for massless topological black holes

International Nuclear Information System (INIS)

Aros, Rodrigo; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge

2003-01-01

An exact expression for the quasinormal modes of scalar perturbation on a massless topological black hole in four and higher dimensions is presented. The massive scalar field is nonminimally coupled to the curvature, and the horizon geometry is assumed to have a negative constant curvature

Higgs mass upper bound in the O(4) approximation

International Nuclear Information System (INIS)

Lin, L.

1991-01-01

In this paper the theoretical breakdown of the minimal standard model in four dimension is investigated when the mass of the Higgs particle is larger than the weak interaction scale. The triviality arguement for an upper bound on the Higgs mass is made quantitative on the lattice in large scale simulations of the spontaneously broken Higgs sector. The authors obtain an upper bound m H ≅640 GeV on the Higgs mass at a dimensionless correlation length ξ = 2 in lattice units.units

Cubic interaction in extended theories of massless higher-spin fields

Energy Technology Data Exchange (ETDEWEB)

Fradkin, E S; Vasiliev, M A

1987-08-17

A cubic interaction of all massless higher-spin fields with s greater than or equal to 1 is constructed, based on the extended higher-spin superalgebras suggested previously by one of us (M.V.). This interaction incorporates gravitational and Yang-Mills interactions of massless higher-spin fields, which turn out to be consistent in the cubic order. An essential novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. An explicit form is found for deformed higher-spin gauge transformations leaving the action invariant.

Bound and rebound states

International Nuclear Information System (INIS)

Orzalesi, C.A.

1979-01-01

In relativistic quantum theory, bound states generate forces in the crossed channel; such forces can affect the binding and self-consistent solutions should be sought for the bound-state problem. The author investigates how self-consistency can be achieved by successive approximations, in a simple scalar model and with successive relativistic eikonal approximations (EAs). Within the generalized ladder approximation, some exact properties of the resulting ''first generation'' bound states are discussed. The binding energies in this approximation are rather small even for rather large values of the primary coupling constant. The coupling of the constituent particles to the first-generation reggeon is determined by a suitable EA and a new generalized ladder amplitude is constructed with rungs given either by the primary gluons or by the first-generation reggeons. The resulting new (second-generation) bound states are found in a reggeized EA. The size of the corrections to the binding energies due to the rebinding effects is surprisingly large. The procedure is then iterated, so as to find - again in an EA - the third-generation bound states. The procedure is found to be self-consistent already at this stage: the third-generation bound states coincide with those of second generation, and no further rebinding takes place in the higher iterations of the approximation method. Features - good and bad - of the model are discussed, as well as the possible relevance of rebinding mechanisms in hadron dynamics. (author)

Massless particles, electromagnetism, and Rieffel induction

International Nuclear Information System (INIS)

Landsman, N.P.; Wiedemann, U.A.

1994-06-01

The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincare groups is re-examined in the massless case. In the situation relevant to physics, it is found that these are related by Marsden-Weinstein reduction with respect to a gauge group. An analogous phenomenon is observed for classical massless relativistic particles. This symplectic reduction procedure can be ('second') quantized using a generalization of the Rieffel induction technique in operator algebra theory, which is carried through in detail for electromagnetism. Starting from the so-called Fermi representation of the field algebra generated by the free abelian gauge field, we construct a new ('rigged') sesquilinear form on the representation space, which is positive semi-definite, and given in terms of a Gaussian weak distribution (promeasure) on the gauge group (taken to be a Hilbert Lie group). This eventually constructs the algebra of observables of quantum electromagnetism (directly in its vacuum representation) as a representation of the so-called algebra of weak observables induced by the trivial representation of the gauge group. (orig.)

Hadrons in two-dimensional quantum chromodynamics: Construction and study of bound states by means of perturbative and non-perturbative methods

International Nuclear Information System (INIS)

Zeppenfeld, D.

1984-01-01

The present thesis deals with the construction and the analysis of mesonic bound states in SU(N) gauge theories in a two-dimensional space-time. The based field theory can thereby be considered as a simplified version of the QCD, the theory of the strong interactions. After an extensive discussion of the quantization in the temporal gauge and after the Poincare invariance of the theory has been shown mesonic bound states and the meson spectrum for different ranges of the free parameters of the theory (quark mass, coupling constant, and index N of the gauge group) are treated. The spectrum is given by a boundary value problem which in the perturbative limit is solved analytically. For massless quarks gauge-invariant annihilation operators are constructed which permit an exact solution of the energy eigenvalue equation. The energy eigenstates so found described massive interacting mesons which are surrounded by a cloud of massless free particles. (orig.) [de

Renormalization problem in nonrenormalizable massless PHI4 theory

International Nuclear Information System (INIS)

Symanzik, K.

1975-05-01

Nonrenormalizable massless PHI 4 theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers of g and gsup(2/epsilon) obtained for the Green's functions in massless (PHI 4 )sub(4 + epsilon) with generic epsilon. For epsilon = 1 and epsilon = 2, these series reduce to double series in powers of g and ln g. The problems of extension to (PHI 4 )sub(4 + epsilon) with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed. (orig.) [de

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

International Nuclear Information System (INIS)

Yarmohammadi, Mohsen; Zareyan, Malek

2016-01-01

In graphene, conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature. For this reason, the bounding of electrons in graphene in the form of geometries of quantum dots is impossible. In gapless graphene, due to its unique electronic band structure, there is a minimal conductivity at Dirac points, that is, in the limit of zero doping. This creates a problem for using such a highly motivated new material in electronic devices. One of the ways to overcome this problem is the creation of a band gap in the graphene band structure, which is made by inversion symmetry breaking (symmetry of sublattices). We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for “local chemical potential” and “local gap”. The calculated energy spectrum exhibits quite different features with and without the perturbations. A characteristic equation for bound states (BSs) has been obtained. It is surprisingly found that the relation between the radial functions of sublattices wave functions, i.e., , , and , , can be established by SO (2) group. (paper)

Single twistor description of massless, massive, AdS, and other interacting particles

International Nuclear Information System (INIS)

Bars, Itzhak; Picon, Moises

2006-01-01

The Penrose transform between twistors and the phase space of massless particles is generalized from the massless case to an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or nonrelativistic, interacting or noninteracting, in flat space or curved spaces. Our unified construction involves always the same twistor Z A with only four complex degrees of freedom and subject to the same helicity constraint. Only the twistor to phase space transform differs from one case to another. Hence, a unification of diverse particle dynamical systems is displayed by the fact that they all share the same twistor description. Our single twistor approach seems to be rather different and a strikingly economical construction of twistors compared to other past approaches that introduced multiple twistors to represent some similar but far more limited set of particle phase space systems

Semiclassical and quantum field theoretic bounds for traversable Lorentzian stringy wormholes

International Nuclear Information System (INIS)

Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya

2004-01-01

A lower bound on the size of a Lorentzian wormhole can be obtained by semiclassically introducing the Planck cutoff on the magnitude of tidal forces (Horowitz-Ross constraint). Also, an upper bound is provided by the quantum field theoretic constraint in the form of the Ford-Roman Quantum Inequality for massless minimally coupled scalar fields. To date, however, exact static solutions belonging to this scalar field theory have not been worked out to verify these bounds. To fill this gap, we examine the wormhole features of two examples from the Einstein frame description of the vacuum low energy string theory in four dimensions which is the same as the minimally coupled scalar field theory. Analyses in this paper support the conclusion of Ford and Roman that wormholes in this theory can have sizes that are indeed only a few order of magnitudes larger than the Planck scale. It is shown that the two types of bounds are also compatible. In the process, we point out a 'wormhole' analog of naked black holes

Loop expansion in massless three-dimensional QED

International Nuclear Information System (INIS)

Guendelman, E.I.; Radulovic, Z.M.

1983-01-01

It is shown how the loop expansion in massless three-dimensional QED can be made finite, up to three loops, by absorbing the infrared divergences in a gauge-fixing term. The same method removes leading and first subleading singularities to all orders of perturbation theory, and all singularities of the fermion self-energy to four loops

Translation-invariant global charges in a local scattering theory of massless particles

International Nuclear Information System (INIS)

Strube, D.

1989-01-01

The present thesis is dedicated to the study for specifically translation-invariant charges in the framework of a Wightman field theory without mass gap. The aim consists thereby in the determination of the effect of the charge operator on asymptotic scattering states of massless particles. In the first section the most important results in the massive case and of the present thesis in the massless case are presented. The object of the second section is the construction of asymptotic scattering states. In the third section the charge operator, which is first only defined on strictly local vectors, is extended to these scattering states, on which it acts additively. Finally an infinitesimal transformation of scalar asymptotic fields is determined. By this for the special case of translation-invariant generators and scalar massless asymptotic fields the same results is present as in the massive case. (orig./HSI) [de

Nonplanar loops leave the Veneziano model photon massless

NARCIS (Netherlands)

Foda, O.

1987-01-01

The absence of a pole at p2=0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found.

Nonplanar loops leave the Veneziano model photon massless

International Nuclear Information System (INIS)

Foda, O.

1987-01-01

The absence of a pole at p 2 =0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found. (orig.)

Nonplanar loops leave the Veneziano model photon massless

Energy Technology Data Exchange (ETDEWEB)

Foda, O.

1987-04-16

The absence of a pole at p/sup 2/=0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found.

Extended higher-spin superalgebras and their massless representations

Energy Technology Data Exchange (ETDEWEB)

Konstein, S E; Vasiliev, M A [AN SSSR, Moscow (USSR). Fizicheskij Inst.

1990-02-12

Three two-parameter sequences of infinite-dimensional extended higher-spin superalgebras are constructed, which give rise to consistent equations of motion of interacting gauge fields of all spins in four dimensions. In the Yang-Mills sector of spin-1 gauge fields, these higher-spin superalgebras reduce to u(n) + u(m), o(n) + o(m) and usp(n) + usp(m) with arbitrary integer parameters n {ge} 0 and m {ge} 0 (n and m are assumed to be even for symplectic algebras). Massless unitary representations of the proposed higher-spin superalgebras are analyzed. It is shown that all these superalgebras obey the admissibility condition which requires them to possess massless unitary representations with just the same spectra of spins as follows from the structure of the related higher-spin gauge fields. We argue that the infinite-dimensional (super)algebras listed in this article classify all possible higher-spin rigid (super)symmetries in four dimensions. (orig.).

Internal space-time symmetries of massive and massless particles and their unification

International Nuclear Information System (INIS)

Kim, Y.S.

2001-01-01

It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted also that, while the rotational degree of freedom for a massless particle leads to its helicity, the two translational degrees of freedom correspond to its gauge degrees of freedom. It is shown that the E(2)-like symmetry of of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like symmetry of massive particles. This mechanism is illustrated in terms of a sphere elongating into a cylinder. In this way, the helicity degree of freedom remains invariant under the Lorentz boost, but the transverse rotational degrees of freedom become contracted into the gauge degree of freedom

Super-acceleration from massless, minimally coupled phi sup 4

CERN Document Server

Onemli, V K

2002-01-01

We derive a simple form for the propagator of a massless, minimally coupled scalar in a locally de Sitter geometry of arbitrary spacetime dimension. We then employ it to compute the fully renormalized stress tensor at one- and two-loop orders for a massless, minimally coupled phi sup 4 theory which is released in Bunch-Davies vacuum at t=0 in co-moving coordinates. In this system, the uncertainty principle elevates the scalar above the minimum of its potential, resulting in a phase of super-acceleration. With the non-derivative self-interaction the scalar's breaking of de Sitter invariance becomes observable. It is also worth noting that the weak-energy condition is violated on cosmological scales. An interesting subsidiary result is that cancelling overlapping divergences in the stress tensor requires a conformal counterterm which has no effect on purely scalar diagrams.

The gravitational shock wave of a massless particle

NARCIS (Netherlands)

Hooft, G. 't; Dray, T

1985-01-01

The (spherical) gravitational shock wave due to a massless particle moving at the speed of light along the horizon of the Schwarzchild black hole is obtained. Special cases of our procedure yield previous results by Aichelburg and Sexl[1] for a photon in Minkowski vpace and by Penrose [2] for

Gravitational interaction of massless higher-spin fields

Energy Technology Data Exchange (ETDEWEB)

Fradkin, E S; Vasiliev, M A

1987-04-30

We show that, despite a widespread belief, the gravitational interaction of massless higher-spin fields (s>2) does exist at least in the first nontrivial order. The principal novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. Our construction is based on an infinite-dimensional higher-spin superalgebra proposed previously that leads to an infinite system of all spins s>1.

Behaviour of Charged Spinning Massless Particles

Directory of Open Access Journals (Sweden)

Ivan Morales

2017-12-01

Full Text Available We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the latter being conserved when the external field is stationary. We also write the conservation laws for the linear and angular momenta. Finally, we find that the particle’s velocity may differ from c as a result of the spin—electromagnetic field interaction, without jeopardizing Lorentz invariance.

How to translate a massless particle (the Weyl neutrino)

International Nuclear Information System (INIS)

Berger, S.B.

1979-01-01

Previous work indicated a deep connection between translations and rotations for a Weyl neutrino (a massless particle). In the letter the explicit form of a translation in the z-direction is given assuming a translation operator of the form esup(i anti g.anti x). (author)

The massless supersymmetric ladder with L rungs

International Nuclear Information System (INIS)

Rossi, G.C.; Stanev, Ya.S.

2009-01-01

We show that in the massless N=1 supersymmetric Wess-Zumino theory it is possible to devise a computational strategy by which the x-space calculation of the ladder 4-point correlators can be carried out without introducing any regularization. As an application we derive a representation valid at all loop orders in terms of conformal invariant integrals. We obtain an explicit expression of the 3-loop ladder diagram for collinear external points

Coulomb Scattering in the Massless Nelson Model III: Ground State Wave Functions and Non-commutative Recurrence Relations

Science.gov (United States)

Dybalski, Wojciech; Pizzo, Alessandro

2018-02-01

Let $H_{P,\\sigma}$ be the single-electron fiber Hamiltonians of the massless Nelson model at total momentum $P$ and infrared cut-off $\\sigma>0$. We establish detailed regularity properties of the corresponding $n$-particle ground state wave functions $f^n_{P,\\sigma}$ as functions of $P$ and $\\sigma$. In particular, we show that \\[ |\\partial_{P^j}f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)|, \\ \\ |\\partial_{P^j} \\partial_{P^{j'}} f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)| \\leq \\frac{1}{\\sqrt{n!}} \\frac{(c\\lambda_0)^n}{\\sigma^{\\delta_{\\lambda_0}}} \\prod_{i=1}^n\\frac{ \\chi_{[\\sigma,\\kappa)}(k_i)}{|k_i|^{3/2}}, \\] where $c$ is a numerical constant, $\\lambda_0\\mapsto \\delta_{\\lambda_0}$ is a positive function of the maximal admissible coupling constant which satisfies $\\lim_{\\lambda_0\\to 0}\\delta_{\\lambda_0}=0$ and $\\chi_{[\\sigma,\\kappa)}$ is the (approximate) characteristic function of the energy region between the infrared cut-off $\\sigma$ and the ultraviolet cut-off $\\kappa$. While the analysis of the first derivative is relatively straightforward, the second derivative requires a new strategy. By solving a non-commutative recurrence relation we derive a novel formula for $f^n_{P,\\sigma}$ with improved infrared properties. In this representation $\\partial_{P^{j'}}\\partial_{P^{j}}f^n_{P,\\sigma}$ is amenable to sharp estimates obtained by iterative analytic perturbation theory in part II of this series of papers. The bounds stated above are instrumental for scattering theory of two electrons in the Nelson model, as explained in part I of this series.

Renormalization and operator product expansion in theories with massless particles

International Nuclear Information System (INIS)

Anikin, S.A.; Smirnov, V.A.

1985-01-01

Renormalization procedure in theories including massless particles is presented. With the help of counterterm formalism the operator product expansion for arbitrary composite fields is derived. The coefficient functions are explicitly expressed in terms of certain Green's functions. (author)

Conformally covariant massless spin-two field equations

International Nuclear Information System (INIS)

Drew, M.S.; Gegenberg, J.D.

1980-01-01

An explicit proof is constructed to show that the field equations for a symmetric tensor field hsub(ab) describing massless spin-2 particles in Minkowski space-time are not covariant under the 15-parameter group SOsub(4,2); this group is usually associated with conformal transformations on flat space, and here it will be considered as a global gauge group which acts upon matter fields defined on space-time. Notwithstanding the above noncovariance, the equations governing the rank-4 tensor Ssub(abcd) constructed from hsub(ab) are shown to be covariant provided the contraction Ssub(ab) vanishes. Conformal covariance is proved by demonstrating the covariance of the equations for the equivalent 5-component complex field; in fact, covariance is proved for a general field equation applicable to massless particles of any spin >0. It is shown that the noncovariance of the hsub(ab) equations may be ascribed to the fact that the transformation behaviour of hsub(ab) is not the same as that of a field consisting of a gauge only. Since this is in contradistinction to the situation for the electromagnetic-field equations, the vector form of the electromagnetic equations is cast into a form which can be duplicated for the hsub(ab)-field. This procedure results in an alternative, covariant, field equation for hsub(ab). (author)

Infrared magneto-spectroscopy of two-dimensional and three-dimensional massless fermions: A comparison

Energy Technology Data Exchange (ETDEWEB)

Orlita, M., E-mail: milan.orlita@lncmi.cnrs.fr [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2 (Czech Republic); Faugeras, C.; Barra, A.-L.; Martinez, G.; Potemski, M. [Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, 38042 Grenoble (France); Basko, D. M. [LPMMC UMR 5493, Université Grenoble 1/CNRS, B.P. 166, 38042 Grenoble (France); Zholudev, M. S. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Teppe, F.; Knap, W. [Laboratoire Charles Coulomb (L2C), UMR CNRS 5221, GIS-TERALAB, Université Montpellier II, 34095 Montpellier (France); Gavrilenko, V. I. [Institute for Physics of Microstructures, RAS, Nizhny Novgorod GSP-105 603950 (Russian Federation); Mikhailov, N. N.; Dvoretskii, S. A. [A.V. Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090 (Russian Federation); Neugebauer, P. [Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart (Germany); Berger, C. [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Institut Néel/CNRS-UJF BP 166, F-38042 Grenoble Cedex 9 (France); Heer, W. A. de [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)

2015-03-21

Here, we report on a magneto-optical study of two distinct systems hosting massless fermions—two-dimensional graphene and three-dimensional HgCdTe tuned to the zero band gap condition at the point of the semiconductor-to-semimetal topological transition. Both materials exhibit, in the quantum regime, a fairly rich magneto-optical response, which is composed from a series of intra- and interband inter-Landau level resonances with for massless fermions typical √(B) dependence. The impact of the system's dimensionality and of the strength of the spin-orbit interaction on the optical response is also discussed.

Cubic Interactions of Massless Bosonic Fields in Three Dimensions

Science.gov (United States)

Mkrtchyan, Karapet

2018-06-01

In this Letter, we take the first step towards construction of nontrivial Lagrangian theories of higher-spin gravity in a metriclike formulation in three dimensions. The crucial feature of a metriclike formulation is that it is known how to incorporate matter interactions into the description. We derive a complete classification of cubic interactions for arbitrary triples s1 , s2 , s3 of massless fields, which are the building blocks of any interacting theory with massless higher spins. We find that there is, at most, one vertex for any given triple of spins in 3D (with one exception, s1=s2=s3=1 , which allows for two vertices). Remarkably, there are no vertices for spin values that do not respect strict triangle inequalities and contain at least two spins greater than one. This translates into selection rules for three-point functions of higher-spin conserved currents in two dimensional conformal field theory. Furthermore, universal coupling to gravity for any spin is derived. Last, we argue that this classification persists in arbitrary Einstein backgrounds.

Automated computation of one-loop integrals in massless theories

International Nuclear Information System (INIS)

Hameren, A. van; Vollinga, J.; Weinzierl, S.

2005-01-01

We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory, and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The number of external legs of the loop integrals is not restricted. All calculations are done within dimensional regularization. (orig.)

Dynamics of massless higher spins in the second order in curvatures

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A [International Centre for Theoretical Physics, Trieste (Italy)

1990-04-05

The consistent equations of motion of interacting massless fields of all spins s=0, 1/2, 1, ..., {infinity} are constructed explicitly to the second order of the expansion in powers of the higher spin strengths. (orig.).

Free-Space Optical Communications: Capacity Bounds, Approximations, and a New Sphere-Packing Perspective

KAUST Repository

Chaaban, Anas

2015-04-01

The capacity of the intensity-modulation direct-detection (IM-DD) free-space optical channel is studied. It is shown that for an IM-DD channel with generally input-dependent noise, the worst noise at high SNR is input-independent Gaussian with variance dependent on the input cost. Based on this result, a Gaussian IM-DD channel model is proposed where the noise variance depends on the optical intensity constraints only. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed, which leads to a tighter bound than an existing sphere-packing bound for the channel with only an average intensity constraint. Under both average and peak constraints, it yields bounds that characterize the high SNR capacity within a negligible gap, where the achievability is proved by using a truncated Gaussian input distribution. This completes the high SNR capacity characterization of the channel, by closing the gap in the existing characterization for a small average-to-peak ratio. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of significant practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions. Finally, the capacity/SNR loss between heterodyne detection (HD) systems and IM-DD systems is bounded at high SNR, where it is shown that the loss grows as SNR increases for a complex-valued HD system, while it is bounded by 1.245 bits or 3.76 dB at most for a real-valued one.

Free-Space Optical Communications: Capacity Bounds, Approximations, and a New Sphere-Packing Perspective

KAUST Repository

Chaaban, Anas; Morvan, Jean-Marie; Alouini, Mohamed-Slim

2015-01-01

The capacity of the intensity-modulation direct-detection (IM-DD) free-space optical channel is studied. It is shown that for an IM-DD channel with generally input-dependent noise, the worst noise at high SNR is input-independent Gaussian with variance dependent on the input cost. Based on this result, a Gaussian IM-DD channel model is proposed where the noise variance depends on the optical intensity constraints only. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed, which leads to a tighter bound than an existing sphere-packing bound for the channel with only an average intensity constraint. Under both average and peak constraints, it yields bounds that characterize the high SNR capacity within a negligible gap, where the achievability is proved by using a truncated Gaussian input distribution. This completes the high SNR capacity characterization of the channel, by closing the gap in the existing characterization for a small average-to-peak ratio. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of significant practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions. Finally, the capacity/SNR loss between heterodyne detection (HD) systems and IM-DD systems is bounded at high SNR, where it is shown that the loss grows as SNR increases for a complex-valued HD system, while it is bounded by 1.245 bits or 3.76 dB at most for a real-valued one.

Local approximation of a metapopulation's equilibrium.

Science.gov (United States)

Barbour, A D; McVinish, R; Pollett, P K

2018-04-18

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

Variational Gaussian approximation for Poisson data

Science.gov (United States)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Vacuum polarization of massless fields in black holes

International Nuclear Information System (INIS)

Zel'nikov, A.I.; Frolov, V.P.

1987-01-01

This chapter contains a detailed survey of the fundamental results from an investigation of the contribution of massless fields to vacuum polarization near black holes. A method is developed for calculating the vacuum average energy-momentum tensor for the electromagnetic field on the surface of a black hole. An explicit value is derived for the renormalized energy-momentum tensor of an electromagnetic field near the event horizon of a rotating black hole

Instanton density in a theory with massless quarks

International Nuclear Information System (INIS)

Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.

1979-01-01

Effect of the complex structure of the QCD vacuum on the density of small-sized instantons is discussed. The method which allows to account for this effect of vacuum quark and gluon condensate is developed. Evaluation of the instanton density is given in the framework of the theory with one, two or three massless quarks. The results of the paper are presented for the cases of SU(2) and SU(3) color groups

Instantons and Massless Fermions in Two Dimensions

Science.gov (United States)

Callan, C. G. Jr.; Dashen, R.; Gross, D. J.

1977-05-01

The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.

The massless two-loop two-point function

International Nuclear Information System (INIS)

Bierenbaum, I.; Weinzierl, S.

2003-01-01

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter ε. As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals. (orig.)

Spikes and matter inhomogeneities in massless scalar field models

International Nuclear Information System (INIS)

Coley, A A; Lim, W C

2016-01-01

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) G 2 stiff fluid spike models both heuristically and numerically, and give a new exact OT G 2 stiff fluid spike solution. We then present a new two-parameter family of non-OT G 2 stiff fluid spike solutions, obtained by the generalization of non-OT G 2 vacuum spike solutions to the stiff fluid case by applying Geroch’s transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT G 2 stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes. (paper)

Thin-wall approximation in vacuum decay: A lemma

Science.gov (United States)

Brown, Adam R.

2018-05-01

The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.

Gauge-invariant dressed fermion propagator in massless QED3

International Nuclear Information System (INIS)

Mitra, Indrajit; Ratabole, Raghunath; Sharatchandra, H.S.

2006-01-01

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED 3 is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement

Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits

Energy Technology Data Exchange (ETDEWEB)

Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics

1975-03-01

General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.

Multi-flavor massless QED{sub 2} at finite densities via Lefschetz thimbles

Energy Technology Data Exchange (ETDEWEB)

Tanizaki, Yuya [RIKEN BNL Research Center, Brookhaven National Laboratory,Upton, NY 11973-5000 (United States); Tachibana, Motoi [Department of Physics, Saga University,Saga 840-8502 (Japan)

2017-02-15

We consider multi-flavor massless (1+1)-dimensional QED with chemical potentials at finite spatial length and the zero-temperature limit. Its sign problem is solved using the mean-field calculation with complex saddle points.

Partially-massless higher-spin algebras and their finite-dimensional truncations

International Nuclear Information System (INIS)

Joung, Euihun; Mkrtchyan, Karapet

2016-01-01

The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS d+1 are studied. The algebras involving PM generators up to depth 2 (ℓ−1) are defined as the maximal symmetries of free conformal scalar field with 2 ℓ order wave equation in d dimensions. We review the construction of these algebras by quotienting certain ideals in the universal enveloping algebra of (A)dS d+1 isometries. We discuss another description in terms of Howe duality and derive the formula for computing trace in these algebras. This enables us to explicitly calculate the bilinear form for this one-parameter family of algebras. In particular, the bilinear form shows the appearance of additional ideal for any non-negative integer values of ℓ−d/2 , which coincides with the annihilator of the one-row ℓ-box Young diagram representation of so d+2 . Hence, the corresponding finite-dimensional coset algebra spanned by massless and PM generators is equivalent to the symmetries of this representation.

Parity violation and the masslessness of the neutrino

International Nuclear Information System (INIS)

Mannheim, P.D.

1978-09-01

It is proposed that the weak interaction be obtained by gauging the strong interaction chiral flavor group. The neutrinos are then four-component spinors. Pairs of right-handed neutrinos are allowed to condense into the vacuum. This produces maximal parity violation in both the quark and lepton sectors of the weak interaction, keeps the neutrinos massless, and also leads to the conventional Weinberg mixing pattern. The approach also in principle provides a way of calculating the Cabibbo angle. 11 references

Parity violation and the masslessness of the neutrino

Energy Technology Data Exchange (ETDEWEB)

Mannheim, P.D.

1978-09-01

It is proposed that the weak interaction be obtained by gauging the strong interaction chiral flavor group. The neutrinos are then four-component spinors. Pairs of right-handed neutrinos are allowed to condense into the vacuum. This produces maximal parity violation in both the quark and lepton sectors of the weak interaction, keeps the neutrinos massless, and also leads to the conventional Weinberg mixing pattern. The approach also in principle provides a way of calculating the Cabibbo angle. 11 references.

Bound-state problem in the light-front Tamm-Dancoff approximation: Numerical study in 1+1 dimensions

International Nuclear Information System (INIS)

Harindranath, A.; Perry, R.J.; Shigemitsu, J.

1992-01-01

Numerical solutions to the two-fermion bound-state problem in the (1+1)-dimensional Yukawa model are presented within the lowest-order light-front Tamm-Dancoff approximation (i.e., keeping only two-fermion and two-fermion--one-boson sectors). Our motivation is twofold. First, we want to understand the dynamics of the model from the very-weak-coupling domain, where the system is governed by nonrelativistic dynamics, to moderate and strong-coupling domains where retardation and self-energy effects become important. Second, we want to develop techniques for solving coupled Tamm-Dancoff integral equations, in particular, methods that can be generalized to higher-order Tamm-Dancoff approximations. To achieve the first goal we first simplify the problem considerably (from a numerical point of view) by the explicit elimination of the higher Fock-space sector. The resulting integral equation, whose kernel depends upon the invariant mass of the state, is solved for the coupling constant, for a given set of the invariant mass and fermion and boson mass parameters. To achieve the second goal we solve the coupled set of equations using both basis functions and direct-discretization techniques. Results from these more general techniques are compared with the explicit-elimination method

Zero-mode effects in the lattice thermodynamics of massless bose field

International Nuclear Information System (INIS)

Gorenstein, M.I.; Lipskikh, S.I.; Sorin, A.S.

1985-01-01

The thermodynamics of free massless Bose field on a lattice is discussed. The coefficients characterizing the finite size effects are obtained. The use of these coefficients in the Yang-Mills thermodynamics allows one to make Monte-Carlo calculations, carried out on the different size lattices, self-consistent

Spectral asymmetry of the massless Dirac operator on a 3-torus

International Nuclear Information System (INIS)

Downes, Robert J.; Vassiliev, Dmitri; Levitin, Michael

2013-01-01

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant

Massless versus Kaluza-Klein gravitons at the LHC

International Nuclear Information System (INIS)

Calmet, Xavier; Aquino, Priscila de; Rizzo, Thomas G.

2010-01-01

We show that the LHC will be able to differentiate between a four-dimensional model with quantum gravity at ∼1 TeV where the (massless) graviton becomes strongly coupled to standard model particles at 1 TeV and brane world type models with a large extra-dimensional volume and massive Kaluza-Klein gravitons. We estimate that the 14 TeV LHC could put a limit of the order of ∼5 TeV on the four-dimensional Planck mass in a model independent way.

Finite energy bounds for $\\piN$ scattering

CERN Document Server

Grassberger, P; Schwela, D

1974-01-01

Upper bounds on energy averaged pi N cross sections are given. Using low energy data and data from pi N backward scattering and NN to pi pi annihilation, it is found that sigma /sub tot/approximately=80 mb and sigma /sub inel/approximately=30 mb, for energies just above the phase-shift region. The bounds are based on assumptions similar to those underlying Froissart's bound and are equal to it asymptotically. However, at finite but large energies, they increase much slower than what might have been anticipated on purely numerological grounds. Related problems in pp and Kp scattering are also discussed. (25 refs) .

Gauge dependence of the infrared behaviour of massless QED3

International Nuclear Information System (INIS)

Mitra, Indrajit; Ratabole, Raghunath; Sharatchandra, H.S.

2006-01-01

Using the Zumino identities it is shown that in a class of non-local gauges, massless QED 3 has an infrared behaviour of a conformal field theory with a continuously varying anomalous dimension of the fermion. In the usual Lorentz gauge, the fermion propagator falls off exponentially for a large separation, but this apparent fermion mass is a gauge artifact

Approximation properties of haplotype tagging

Directory of Open Access Journals (Sweden)

Dreiseitl Stephan

2006-01-01

Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

IR finite one-loop box scalar integral with massless internal lines

International Nuclear Information System (INIS)

Duplancic, G.; Nizic, B.

2002-01-01

The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments. (orig.)

Upper and lower bounds in nonrelativistic scattering theory

International Nuclear Information System (INIS)

Darewych, J.W.; Pooran, R.

1980-01-01

We consider the problem of determining rigorous upper and lower bounds to the difference between the exact and approximate scattering phase shift, for the case of central potential scattering. The present work is based on the Kato identities and the phase-amplitude formalism of potential scattering developed by Calogero. For nonstationary approximations, a new first-order (in small quantities) bound is established which is particularly useful for partial waves other than s waves. Similar, but second-order, bounds are established for approximations which are stationary. Some previous results, based on the use of the Lippman--Schwinger equation are generalized, and some new bounds are established. These are illustrated, and compared to previous results, by a simple example. We discuss the advantages and disadvantages of the present results in comparison to those derived previously. Finally, we present the generalization of some of the present formalism to the case of many-channel scattering involving many-particle systems, and discuss some of the difficulties of their practical implementation

Bounds on graviton mass using weak lensing and SZ effect in galaxy clusters

Science.gov (United States)

Rana, Akshay; Jain, Deepak; Mahajan, Shobhit; Mukherjee, Amitabha

2018-06-01

In General Relativity (GR), the graviton is massless. However, a common feature in several theoretical alternatives of GR is a non-zero mass for the graviton. These theories can be described as massive gravity theories. Despite many theoretical complexities in these theories, on phenomenological grounds the implications of massive gravity have been widely used to put bounds on graviton mass. One of the generic implications of giving a mass to the graviton is that the gravitational potential will follow a Yukawa-like fall off. We use this feature of massive gravity theories to probe the mass of graviton by using the largest gravitationally bound objects, namely galaxy clusters. In this work, we use the mass estimates of galaxy clusters measured at various cosmologically defined radial distances measured via weak lensing (WL) and Sunyaev-Zel'dovich (SZ) effect. We also use the model independent values of Hubble parameter H (z) smoothed by a non-parametric method, Gaussian process. Within 1σ confidence region, we obtain the mass of graviton mg 6.82 Mpc from weak lensing and mg 5.012 Mpc from SZ effect. This analysis improves the upper bound on graviton mass obtained earlier from galaxy clusters.

Interacting massless scalar and source-free electromagnetic fields

International Nuclear Information System (INIS)

Ayyangar, B.R.N.; Mohanty, G.

1985-01-01

The relativistic field equations for interacting massless attractive scalar and source-free electromagnetic fields in a cylindrically symmetric spacetime of one degree of freedom with reflection symmetry have been reduced to a first order implicit differential equation depending on time which enables one to generate a class of solution to the field equations. The nature of the scalar and electromagnetic fields is discussed. It is shown that the geometry of the spacetime admits of an irrotational stiff fluid distribution without prejudice to the interacting electromagnetic fields. 10 refs. (author)

Asymptotic fermion propagator in massless three-dimensional QED

International Nuclear Information System (INIS)

Hand, B.J.

1993-01-01

Massless quantum electrodynamics in two spatial and one time dimensions has a logarithmically confining static Coulomb potential, and thus nontrivial infrared behavior. We apply a technique developed for ordinary four-dimensional quantum electrodynamics in which the charged asymptotic states in the theory are dressed with soft vector bosons, in order to improve the representation of the infrared dynamics in perturbation theory. The resulting modification to the mass-shell behavior of the fermion propagator is determined, with the result that the propagator no longer possesses a mass-shell singularity

All-order results for infrared and collinear singularities in massless gauge theories

CERN Document Server

Dixon, Lance J; Magnea, Lorenzo

2010-01-01

We review recent results concerning the all-order structure of infrared and collinear divergences in massless gauge theory amplitudes. While the exponentiation of these divergences for nonabelian gauge theories has been understood for a long time, in the past couple of years we have begun to unravel the all-order structure of the anomalous dimensions that build up the perturbative exponent. In the large-Nc limit, all infrared and collinear divergences are determined by just three functions; one of them, the cusp anomalous dimension, plays a key role also for non-planar contributions. Indeed, all infrared and collinear divergences of massless gauge theory amplitudes with any number of hard partons may be captured by a surprisingly simple expression constructed as a sum over color dipoles. Potential corrections to this expression, correlating four or more hard partons at three loops or beyond, are tightly constrained and are currently under study.

Partially massless higher-spin theory II: one-loop effective actions

Energy Technology Data Exchange (ETDEWEB)

Brust, Christopher [Perimeter Institute for Theoretical Physics,31 Caroline St. N, Waterloo, Ontario, N2L 2Y5 (Canada); Hinterbichler, Kurt [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH, 44106 (United States)

2017-01-30

We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D=7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D=4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D=4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.

Partially massless higher-spin theory II: one-loop effective actions

International Nuclear Information System (INIS)

Brust, Christopher; Hinterbichler, Kurt

2017-01-01

We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D=7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D=4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D=4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.

Bounds on the charmed particles masses from the Ksub(L) → 2μ decay width and Ksub(L)-Ksub(S) mass difference in an asymptotically free theory of strong interactions

International Nuclear Information System (INIS)

Vainshtein, A.I.; Zakharov, V.I.; Novikov, V.A.; Shifman, M.A.

1975-01-01

Bounds on the masses of charmed particles are derived from the calculation of the amplitudes of the Ksub(L) → 2μ and Ksub(L)-Ksub(S) transitions within the framework of the Weinberg-Salam model. The strong interactions are assumed to be connected with the color SU(3) group and mediated by octet of massless gluons. The account of strong interactions is shown to have almost no effect on the bound on the masses of charmed particles μsub(c). From the Ksub(L) → 2μ decay rate the upper bound on μsub(c) is μsub(c) (<=) 8 GeV, and from the Ksub(L)-Ksub(S) mass difference the bound is found to be μsub(c) (<=) 2.3 GeV

Coupled kinetic equations for fermions and bosons in the relaxation-time approximation

Science.gov (United States)

Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw

2018-02-01

Kinetic equations for fermions and bosons are solved numerically in the relaxation-time approximation for the case of one-dimensional boost-invariant geometry. Fermions are massive and carry baryon number, while bosons are massless. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions, which specify the coupling between the fermionic and bosonic sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a nonequilibrium mixture of fermions and bosons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of fermion and boson components, while the bulk viscosity is given by the formula known for a gas of fermions, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture, provided fermions are massive. We further observe the hydrodynamization effect, which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behavior is connected with the existence of an attractor solution for conformal systems.

Quantum mean-field approximations for nuclear bound states and tunneling

International Nuclear Information System (INIS)

Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge

1979-01-01

A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems

Gauge-invariant dressed fermion propagator in massless QED{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Mitra, Indrajit [Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan-Nagar, Kolkata 700064 (India)]. E-mail: indrajit.mitra@saha.ac.in; Ratabole, Raghunath [Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India)]. E-mail: raghu@imsc.res.in; Sharatchandra, H.S. [Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India)]. E-mail: sharat@imsc.res.in

2006-04-27

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED{sub 3} is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.

Unusual expression of tension of a massless cable with application to the oscillations of a mass suspended to a cable with a variable length

Science.gov (United States)

Babaz, Mathieu; Jezequel, Louis; Lamarque, Claude-Henri; Perrard, Patrick

2016-02-01

A new approach of cables' dynamics is presented in this paper. It is based on the exact expression of tension coming from continuum mechanics, while the previous elastic models of cables in open literature consider an approximation of small strain which reduces the cable to a linear spring. The equations of a mass suspended to a massless cable are derived on the basis of this new formulation. The problem is studied and numerically calculated for one and two degrees of freedom. A comparison with the classical approach and a nonlinear analysis are presented.

No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes

Directory of Open Access Journals (Sweden)

Shahar Hod

2017-08-01

Full Text Available We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.

The soliton solution of the PHI24 field theory in the Hartree approximation

International Nuclear Information System (INIS)

Altenbokum, M.

1984-01-01

In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de

Computing variational bounds for flow through random aggregates of Spheres

International Nuclear Information System (INIS)

Berryman, J.G.

1983-01-01

Known formulas for variational bounds on Darcy's constant for slow flow through porous media depend on two-point and three-poiint spatial correlation functions. Certain bounds due to Prager and Doi depending only a two-point correlation functions have been calculated for the first time for random aggregates of spheres with packing fractions (eta) up to eta = 0.64. Three radial distribution functions for hard spheres were tested for eta up to 0.49: (1) the uniform distribution or ''well-stirred approximation,'' (2) the Percus Yevick approximation, and (3) the semi-empirical distribution of Verlet and Weis. The empirical radial distribution functions of Benett andd Finney were used for packing fractions near the random-close-packing limit (eta/sub RCP/dapprox.0.64). An accurate multidimensional Monte Carlo integration method (VEGAS) developed by Lepage was used to compute the required two-point correlation functions. The results show that Doi's bounds are preferred for eta>0.10 while Prager's bounds are preferred for eta>0.10. The ''upper bounds'' computed using the well-stirred approximation actually become negative (which is physically impossible) as eta increases, indicating the very limited value of this approximation. The other two choices of radial distribution function give reasonable results for eta up to 0.49. However, these bounds do not decrease with eta as fast as expected for large eta. It is concluded that variational bounds dependent on three-point correlation functions are required to obtain more accurate bounds on Darcy's constant for large eta

Casimir energy of massless fermions in the Slab-bag

International Nuclear Information System (INIS)

Paola, R.D.M. de; Rodrigues, R.B.; Svaiter, N.F.

1999-04-01

The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space-time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta function regularization procedure is used and it is founded that the regularized zero-point energy density is finite for any number of space-time dimensions. We present a general expression for the Casimir energy for the fermionic field in such a situation. (author)

On the conformal transformations in the massless Thirring model

International Nuclear Information System (INIS)

Hadjiivanov, L.K.; Mikhov, S.G.; Stoyanov, D.T.

1977-01-01

On the basis of solutions for the massless scalar field in the two dimensional space-time the fields satisfying the renormalized Thirring equation are constructed. Both infinitesimal and global transformations with respect to the two-dimensional conformal group for these fields are obtained. The latter do not coincide with the standard ones. The renormalized Thirring equation is proved to be covariant under infinitesimal conformal group transformations as well as under the global transformations belonging to the universal covering of the conformal group

Massless fields in curved space-time: The conformal formalism

International Nuclear Information System (INIS)

Castagnino, M.A.; Sztrajman, J.B.

1986-01-01

A conformally invariant theory for massless quantum fields in curved space-time is formulated. We analyze the cases of spin-0, - 1/2 , and -1. The theory is developed in the important case of an ''expanding universe,'' generalizing the particle model of ''conformal transplantation'' known for spin-0 to spins- 1/2 and -1. For the spin-1 case two methods introducing new conformally invariant gauge conditions are stated, and a problem of inconsistency that was stated for spin-1 is overcome

Massless phases and confinement in extended Z(4) gauge theories

International Nuclear Information System (INIS)

Alcaraz, F.C.; Jacobs, L.

1983-01-01

We analyze a general Z(4) lattice gauge theory in four dimensions. The two-parameter model is shown to possess four distinct phases characterized by the behavior of Wilson loops carrying one or two units of flux. The appearance of a bifurcation in the phase plane just below the Wilson action is conjectured to be the precursor of the massless electrodynamicslike phase seen in the larger-N models

Approximate estimation of system reliability via fault trees

International Nuclear Information System (INIS)

Dutuit, Y.; Rauzy, A.

2005-01-01

In this article, we show how fault tree analysis, carried out by means of binary decision diagrams (BDD), is able to approximate reliability of systems made of independent repairable components with a good accuracy and a good efficiency. We consider four algorithms: the Murchland lower bound, the Barlow-Proschan lower bound, the Vesely full approximation and the Vesely asymptotic approximation. For each of these algorithms, we consider an implementation based on the classical minimal cut sets/rare events approach and another one relying on the BDD technology. We present numerical results obtained with both approaches on various examples

Exact spinor-scalar bound states in a quantum field theory with scalar interactions

International Nuclear Information System (INIS)

Shpytko, Volodymyr; Darewych, Jurij

2001-01-01

We study two-particle systems in a model quantum field theory in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve for the mediating field in terms of the particle fields. This results in a Hamiltonian in which the mediating-field propagator appears directly in the interaction term. It is shown that exact two-particle eigenstates of the Hamiltonian can be determined. The resulting relativistic fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle limits. Analytical solutions for the bound state energy spectrum are obtained for the case of massless mediating fields

On transparent potentials: a Born approximation study

International Nuclear Information System (INIS)

Coudray, C.

1980-01-01

In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy

Variational lower bound on the scattering length

International Nuclear Information System (INIS)

Rosenberg, L.; Spruch, L.

1975-01-01

The scattering length A characterizes the zero-energy scattering of one system by another. It was shown some time ago that a variational upper bound on A could be obtained using methods, of the Rayleigh-Ritz type, which are commonly employed to obtain upper bounds on energy eigenvalues. Here we formulate a method for obtaining a variational lower bound on A. Once again the essential idea is to express the scattering length as a variational estimate plus an error term and then to reduce the problem of bounding the error term to one involving bounds on energy eigenvalues. In particular, the variational lower bound on A is rigorously established provided a certin modified Hamiltonian can be shown to have no discrete states lying below the level of the continuum threshold. It is unfortunately true that necessary conditions for the existence of bound states are not available for multiparticle systems in general. However, in the case of positron-atom scattering the adiabatic approximation can be introduced as an (essentially) solvable comparison problem to rigorously establish the nonexistence of bound states of the modified Hamiltonian. It has recently been shown how the validity of the variational upper bound on A can be maintained when the target ground-state wave function is imprecisely known. Similar methods can be used to maintain the variational lower bound on A. Since the bound is variational, the error in the calculated scattering length will be of second order in the error in the wave function. The use of the adiabatic approximation in the present context places no limitation in principle on the accuracy achievable

Remarks on the paper ''Two-dimensional quantum field theories involving massless particles'' by N.Nakanishi

International Nuclear Information System (INIS)

Stoyanov, D.Ts.

1978-01-01

Some critical remarks on the paper by N.Nakanishi ''Tso-Dimensional Quantum Field Theories Involving Massless Particles'' are presented. It is stated that because of the obtained commutation relations the massless scalar fields of the theory connot have the asymptotic behaviour assumed by N.Nakanishi. The contradiction, appearing in the proof of the irreducibility of the scalar field, is demonstrated. Therefore, the theory constructed by Nakanishi, in which an attempt is made to formulate it with the help of one scalar field and correspondingly with one topological charge, is contradictory. It is shown that the statistics of the solutions is not fixed and the solutions satisfying Bose or Fermi statistics differ by constant operator factors

On the exponentiation of leading infrared divergences in massless Yang-Mills theories

International Nuclear Information System (INIS)

Frenkel, J.; Garcia, R.L.

1977-01-01

We derive, in the axial gauge, the effective U-matrix which governs the behaviour of leading infrared singularities in the self-energy functions of Yang-Mills particles. We then show in a very simple manner, that these divergences, which determine the leading singularities in massless Yang-Mills theories, exponentiate [pt

Massive, massless and ghost modes of gravitational waves from higher-order gravity

DEFF Research Database (Denmark)

Bogdanos, Charalampos; Capozziello, Salvatore; De Laurentis, Mariafelicia

We linearize the field equations for higher order theories that contain scalar invariants other than the Ricci scalar. We find that besides a massless spin-2 field (the standard graviton), the theory contains also spin-0 and spin-2 massive modes with the latter being, in general, ghost modes. Then...

Compound Poisson Approximations for Sums of Random Variables

OpenAIRE

Serfozo, Richard F.

1986-01-01

We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...

New twistorial integral formulas for massless free fields of arbitrary spin

International Nuclear Information System (INIS)

Cardoso, J.G.

1991-01-01

A manifestly scaling-invariant version of the Kirchoff-D'Adhemar-Penrose field integrals is presented. The invariant integral expressions for the spinning massless free fields are directly transcribed into the framework of twistor theory. It is then shown that the resulting twistorial field integrals can be thought of as being equivalent to the universal Penrose contour integral formulas for these fields

Gauge dependence of the infrared behaviour of massless QED{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Mitra, Indrajit [Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan-Nagar, Kolkata 700064 (India)]. E-mail: indrajit.mitra@saha.ac.in; Ratabole, Raghunath [The Institute of Mathematical Sciences, CIT Campus, Taramani PO, Chennai 600113 (India)]. E-mail: raghu@imsc.res.in; Sharatchandra, H.S. [The Institute of Mathematical Sciences, CIT Campus, Taramani PO, Chennai 600113 (India)]. E-mail: sharat@imsc.res.in

2006-03-23

Using the Zumino identities it is shown that in a class of non-local gauges, massless QED{sub 3} has an infrared behaviour of a conformal field theory with a continuously varying anomalous dimension of the fermion. In the usual Lorentz gauge, the fermion propagator falls off exponentially for a large separation, but this apparent fermion mass is a gauge artifact.

Tight Bounds for Distributed Functional Monitoring

DEFF Research Database (Denmark)

Woodruff, David P.; Zhang, Qin

2011-01-01

$, our bound resolves their main open question. Our lower bounds are based on new direct sum theorems for approximate majority, and yield significant improvements to problems in the data stream model, improving the bound for estimating $F_p, p > 2,$ in $t$ passes from $\\tilde{\\Omega}(n^{1-2/p}/(\\eps^{2/p......} t))$ to $\\tilde{\\Omega}(n^{1-2/p}/(\\eps^{4/p} t))$, giving the first bound for estimating $F_0$ in $t$ passes of $\\Omega(1/(\\eps^2 t))$ bits of space that does not use the gap-hamming problem, and showing a distribution for the gap-hamming problem with high external information cost or super...

Involution Requirement on a Boundary Makes Massless Fermions Compactified on a Finite Flat Disk Mass Protected

Science.gov (United States)

Mankoč Borštnik, N. S.; Nielsen, H. B.

2006-12-01

The genuine Kaluza-Klein-like theories--with no fields in addition to gravity--have difficulties with the existence of massless spinors after the compactification of some space dimensions \\cite{witten}. We proposed (Phys. Lett. B 633 (2006)771) such a boundary condition for spinors in 1+5 compactified on a flat disk that ensures masslessness of spinors in d=1+3 as well as their chiral coupling to the corresponding background gauge field (which solves equations of motion for a free field linear in the Riemann curvature). In this paper we study the same toy model: M^{(1+3)} x M^{(2)}, looking this time for an involution which transforms a space of solutions of Weyl equations in d=1+5 from the outside of the flat disk in x^5 and x^6 into its inside, allowing massless spinor of only one handedness--and accordingly assures mass protection--and of one charge--1/2--and infinitely many massive spinors of the same charge, chirally coupled to the corresponding background gauge field. We reformulate the operator of momentum so that it is Hermitean on the vector space of spinor states obeying the involution boundary condition.

Description of the higher massless irreducible integer spins in the BRST approach

International Nuclear Information System (INIS)

Pashnev, A.; Tsulaya, M.

1998-01-01

The BRST approach is applied to the description of irreducible massless higher spins representations of the Poincare group in arbitrary dimensions. The total system of constraints in such theory includes both the first and the second class constraints. The corresponding nilpotent BRST charge contains terms up to the seventh degree in ghosts

Resonant frequencies of massless scalar field in rotating black-brane spacetime

Institute of Scientific and Technical Information of China (English)

Jing Ji-Liang; Pan Qi-Yuan

2008-01-01

This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brahe spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.

Production of massless particles in collisions of strings at high energy

International Nuclear Information System (INIS)

Lipatov, L.N.

1988-01-01

The authors obtain explicit formulas (generalizing the Low-Gribov expressions) for the production amplitude of massless particles (gluons and gravitons) with low transverse momenta in the scattering of lower-mass excitations of open and closed strings. In the limit α' → 0 they reproduce the results of calculation of effective vertices for inelastic scattering amplitudes in multi-Regge kinematics in the Yang-Mills theory and in gravitation

On the bosonization of the massless spinor electrodynamics

International Nuclear Information System (INIS)

Mikhov, S.G.; Stoyanov, D.Ts.

1979-01-01

A method for constructing a field transformed according to a linear representation of a Lie group out of fields transformed nonlinearly under the action of the same group is proposed. This procedure is used in order to construct spinor fields out of tensor ones. Such a ''bosonization'' of the spinor field is used to reformulate the massless spinor electrodynamics in terms of nonlinear tensor fields. It appears in this formulation that the Dirac equation is reduced to a definition of the electromagnetic vector potential in terms of the nonlinear tensor fields and to the current conservations playing the role of a consistency condition for this formulation

Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

Science.gov (United States)

Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

2018-06-01

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions

CERN Document Server

Gelfond, O A

2015-01-01

Interactions of massless fields of all spins in four dimensions with currents of any spin is shown to result from a solution of the linear problem that describes a gluing between rank-one (massless) system and rank-two (current) system in the unfolded dynamics approach. Since the rank-two system is dual to a free rank-one higher-dimensional system, that effectively describes conformal fields in six space-time dimensions, the constructed system can be interpreted as describing a mixture between linear conformal fields in four and six dimensions. Interpretation of the obtained results in spirit of AdS/CFT correspondence is discussed.

Limitations of shallow nets approximation.

Science.gov (United States)

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Approximately dual frames in Hilbert spaces and applications to Gabor frames

OpenAIRE

Christensen, Ole; Laugesen, Richard S.

2011-01-01

Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in...

Approximate Model Checking of PCTL Involving Unbounded Path Properties

Science.gov (United States)

Basu, Samik; Ghosh, Arka P.; He, Ru

We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the existing statistical methods either consider a restricted subset of PCTL, specifically, the subset that can only express bounded until properties; or rely on user-specified finite bound on the sample path length. We propose a new method that does not have such restrictions and can be effectively used to reason about unbounded until properties. We approximate probabilistic characteristics of an unbounded until property by that of a bounded until property for a suitably chosen value of the bound. In essence, our method is a two-phase process: (a) the first phase is concerned with identifying the bound k 0; (b) the second phase computes the probability of satisfying the k 0-bounded until property as an estimate for the probability of satisfying the corresponding unbounded until property. In both phases, it is sufficient to verify bounded until properties which can be effectively done using existing statistical techniques. We prove the correctness of our technique and present its prototype implementations. We empirically show the practical applicability of our method by considering different case studies including a simple infinite-state model, and large finite-state models such as IPv4 zeroconf protocol and dining philosopher protocol modeled as Discrete Time Markov chains.

Approximation of complex algebraic numbers by algebraic numbers of bounded degree

OpenAIRE

Bugeaud, Yann; Evertse, Jan-Hendrik

2007-01-01

We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

Renormalization group analysis of the temperature dependent coupling constant in massless theory

International Nuclear Information System (INIS)

Yamada, Hirofumi.

1987-06-01

A general analysis of finite temperature renormalization group equations for massless theories is presented. It is found that in a direction where momenta and temperature are scaled up with their ratio fixed the coupling constant behaves in the same manner as in zero temperature and that asymptotic freedom at short distances is also maintained at finite temperature. (author)

New anomaly: nonvanishing interaction of longitudinal real photons in massless quantum electrodynamics

International Nuclear Information System (INIS)

Gorskij, A.S.; Ioffe, B.L.; Khodzhamiryan, A.Yu.

1989-01-01

It is shown that in massless electrodynamics (when the electron mass is strictly zero) the cross section of longitudinal photon interaction on mass shell is nonvanishing. The reasons of appearance of this effects and its possible consequences as well as analogous effects in other quantum field theories (especially non-Abelian gauge theories) are discussed. 7 refs.; 2 figs

Space-efficient path-reporting approximate distance oracles

DEFF Research Database (Denmark)

Elkin, Michael; Neiman, Ofer; Wulff-Nilsen, Christian

2016-01-01

We consider approximate path-reporting distance oracles, distance labeling and labeled routing with extremely low space requirements, for general undirected graphs. For distance oracles, we show how to break the nlog⁡n space bound of Thorup and Zwick if approximate paths rather than distances need...

Ordered cones and approximation

CERN Document Server

Keimel, Klaus

1992-01-01

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

(2 + 1)-dimensional interacting model of two massless spin-2 fields as a bi-gravity model

Science.gov (United States)

Hoseinzadeh, S.; Rezaei-Aghdam, A.

2018-06-01

We propose a new group-theoretical (Chern-Simons) formulation for the bi-metric theory of gravity in (2 + 1)-dimensional spacetime which describe two interacting massless spin-2 fields. Our model has been formulated in terms of two dreibeins rather than two metrics. We obtain our Chern-Simons gravity model by gauging mixed AdS-AdS Lie algebra and show that it has a two dimensional conformal field theory (CFT) at the boundary of the anti de Sitter (AdS) solution. We show that the central charge of the dual CFT is proportional to the mass of the AdS solution. We also study cosmological implications of our massless bi-gravity model.

Singletons, higher spin massless states and the supermembrane

International Nuclear Information System (INIS)

Bergshoeff, E.; Salam, A.; Sezgin, E.; Tanii, Yoshiaki.

1988-01-01

We analyse the spectrum of the eleven dimensional supermembrane quantized in AdS 4 xS 7 background. The classical membrane lives at the boundary of AdS 4 which is S 2 xS 1 , and has OSp(8,4) symmetry. We find that the spectrum contains, in addition to the N=8 supersymmetric (massive) singletons (which may possibly be the ultimate preons), also massless states of all higher integer and half-integer spin. These states fill the irreducible representations of OSp(8,4) with highest spin s max =2,4,6,... The s max =2 multiplet corresponds to the states of the de Wit-Nicolai's N=8 gauged supergravity in four dimensions. (author). 24 refs

Analytic continuation of massless two-loop four-point functions

International Nuclear Information System (INIS)

Gehrmann, T.; Remiddi, E.

2002-01-01

We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like 1→3 decay to Minkowskian regions relevant to all 1→3 and 2→2 reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron-positron annihilation. (author)

Unfolded equations for current interactions of 4d massless fields as a free system in mixed dimensions

Energy Technology Data Exchange (ETDEWEB)

Gelfond, O. A., E-mail: gel@lpi.ru [Russian Academy of Sciences, Institute of System Research (Russian Federation); Vasiliev, M. A., E-mail: vasiliev@lpi.ru [Russian Academy of Sciences, I. E. Tamm Department of Theoretical Physics, Lebedev Physical Institute (Russian Federation)

2015-03-15

Interactions of massless fields of all spins in four dimensions with currents of any spin are shown to result from a solution of the linear problem that describes a gluing between a rank-one (massless) system and a rank-two (current) system in the unfolded dynamics approach. Since the rank-two system is dual to a free rank-one higher-dimensional system that effectively describes conformal fields in six space-time dimensions, the constructed system can be interpreted as describing a mixture between linear conformal fields in four and six dimensions. An interpretation of the obtained results in the spirit of the AdS/CFT correspondence is discussed.

Analytic bounds and approximations for annuities and Asian options

NARCIS (Netherlands)

Vanduffel, S.; Shang, Z.; Henrard, L.; Dhaene, J.; Valdez, E.A.

2008-01-01

Even in case of the Brownian motion as most natural rate of return model it appears too difficult to obtain analytic expressions for most risk measures of constant continuous annuities. In literature the so-called comonotonic approximations have been proposed but these still require the evaluation

On the identification of gravitation with the massless spin 2 field

International Nuclear Information System (INIS)

Meszaros, A.

1984-05-01

The identification of gravitation with the massless spin 2 gauge field (the gauge group is the group of translations) requires to restrict the solutions of Einstein's equations to the class of topologically trivial manifolds. It is shown that the validity of this restriction in nature is supported by the present-day empirical facts. The identification has a drastic impact on cosmology, because the fulfilment of the cosmological principle seems to be improbable. (author)

Regularization by Functions of Bounded Variation and Applications to Image Enhancement

International Nuclear Information System (INIS)

Casas, E.; Kunisch, K.; Pola, C.

1999-01-01

Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal-dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise

Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain

Energy Technology Data Exchange (ETDEWEB)

Kitanine, N. [Univ. de Bourgogne (France). IMB, UMR 5584 du CNRS; Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M.; Terras, V. [ENS Lyon (France). UMR 5672 du CNRS, Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Inst., Moscow (Russian Federation)

2011-03-15

We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system size. Moreover, the corresponding amplitudes can be obtained as a product of a ''smooth'' and a ''discrete'' part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a power-law in the system size with the same critical exponents as in the longdistance asymptotic behavior of the related two-point correlation functions. The methods we develop in this article are rather general and can be applied to other massless integrable models associated to the six-vertex R-matrix and having determinant representations for their form factors. (orig.)

Forecasting with Universal Approximators and a Learning Algorithm

DEFF Research Database (Denmark)

Kock, Anders Bredahl

2011-01-01

to the performance of the best single model in the set of models combined from. The use of universal approximators along with a combination scheme for which explicit loss bounds exist should give a solid theoretical foundation to the way the forecasts are performed. The practical performance will be investigated...... combination has a long history in econometrics focus has not been on proving loss bounds for the combination rules applied. We apply the Weighted Average Algorithm (WAA) of Kivinen & Warmuth (1999) for which such loss bounds exist. Specifically, one can bound the worst case performance of the WAA compared...

Forecasting with Universal Approximators and a Learning Algorithm

DEFF Research Database (Denmark)

Kock, Anders Bredahl

bounds for the combination rules applied. We apply the Weighted Average Algorithm (WAA) of Kivinen and Warmuth (1999) for which such loss bounds exist. Specifically, one can bound the worst case performance of the WAA compared to the performance of the best single model in the set of models combined from....... The use of universal approximators along with a combination scheme for which explicit loss bounds exist should give a solid theoretical foundation to the way the forecasts are performed. The practical performance will be investigated by considering various monthly postwar macroeconomic data sets for the G...

Non-Schwinger solution of the two-dimensional massless spinor electrodynamics

International Nuclear Information System (INIS)

Mikhov, S.G.

1981-01-01

In the present paper a regularization procedure is formulated for the current in the two-dimensional massless spinor electrodynamics that is both gauge and γ 5 -gauge invariant. This gives rise to an operator solution of the model that does not involve a massive photon. The latter solution is studied in some detail, and it is shown that although a charge operator exists, it does not define the electric charge of the spinor field. This can be a manifestation of the charge screening mechanism that is present in the Schwinger model [ru

Massless second-order tetradic spin-3 and higher-helicity bosons

Energy Technology Data Exchange (ETDEWEB)

Aragone, C; La Roche, H [Universidad Simon Bolivar, Caracas (Venezuela) Dept. de Fisica

1982-11-21

The unique, uniform, second-order formulation of massless bosons of helicity >=3 is presented here in terms of tetradic fields. The actions we find are shown to coincide both with the first-order (tetradic) formulation of Vasiliev and with the symmetric second-order description of Fronsdal. We carefully analyse the gravitational coupling of the spin-3 field and find that tetradic spin-3 matter presents the same translational consistency problem as symmetric matter does. Furthermore, in the curved tetradic case the generalized Lorentz invariance can be restored by the addition of nominimal terms.

The log-linear return approximation, bubbles, and predictability

DEFF Research Database (Denmark)

Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividendprice ratio. Next, we simulate various rational bubbles which have explosive conditional expec...

Gravitational Collapse of Massless Fields in an Expanding Universe

Directory of Open Access Journals (Sweden)

Yoo Chul-Moon

2018-01-01

Full Text Available Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. The initial data is constructed for a Gaussian like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. The difference of the late time expansion law of the lattice universe depending on the final fate of the gravitational collapse is discussed.

dS/CFT correspondence from a holographic description of massless scalar fields in Minkowski space-time

International Nuclear Information System (INIS)

Loran, Farhang

2004-01-01

We solve Klein-Gordon equation for massless scalars on (d+1)-dimensional Minkowski (Euclidean) space in terms of the Cauchy data on the hypersurface t=0. By inserting the solution into the action of massless scalars in Minkowski (Euclidean) space we obtain the action of dual theory on the boundary t=0 which is exactly the holographic dual of conformally coupled scalars on (d+1)-dimensional (Euclidean anti) de Sitter space obtained in (A)dS/CFT correspondence. The observed equivalence of dual theories is explained using the one-to-one map between conformally coupled scalar fields on Minkowski (Euclidean) space and (Euclidean anti) de Sitter space which is an isomorphism between the hypersurface t=0 of Minkowski (Euclidean) space and the boundary of (A)dS space

Massive spin-one fields from couplings with five massless real scalars

Science.gov (United States)

Bizdadea, Constantin; Cioroianu, Eugen-Mihaita; Saliu, Solange-Odile

2017-12-01

In this paper we implement a new procedure by which one may generate mass for a vector field in the context of its interactions to a system of five real scalar fields. This purpose will be achieved by means of the general multi-step program from [1] adapted to the present situation: (1) we begin with a free theory in four space-time dimensions whose Lagrangian action is given by the sum between the standard Maxwell action and that for a collection consisting in five massless real scalar fields; (2) we construct a general class of gauge theories whose free limit is that from step (1) by means of the deformation of the solution to the master equation [2, 3] with the help of local BRST cohomology [4-6]; (3) we perform some suitable redefinitions of the free parameters that label interacting theories from (2) such that the mass terms become manifest in the new free limit. The outputs of our procedure can be synthesized in: (A) the vector field acquires mass; (B) the scalar fields gain gauge transformations; (C) the gauge algebras of the interacting theories are Abelian; (D) the propagator of the massive vector field emerging from the gauge-fixed actions behaves, in the limit of large Euclidean momenta, like that from the massless case.

The Log-Linear Return Approximation, Bubbles, and Predictability

DEFF Research Database (Denmark)

Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten

2012-01-01

We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional expe...

Infrared behavior of massless field theories

International Nuclear Information System (INIS)

Sapirstein, J.R.

1979-01-01

Typical infrared effects in several gauge field theories with massless particles are investigated in perturbation theory. It is first shown that divergences occurring in individual Feynman graphs arising from integrations over the long-wavelength modes of the fields cancel when the graphs are grouped together in a particular way, in a generalization of the Bloch-Nordsieck treatment of QED. As one of the requirements of finiteness is renormalization of the vector propagator off shell, the charge in these theories is not directly related to classical experiment. In an effort to find the meaning of charge the low-energy theorem is considered. Although in lowest order the graphs reproduce the Thompson limit, it is found that loop corrections are singular in the low-energy limit; a simple definition of the charge is thus precluded. Finally, the behavior of the quark color magnetic moment is treated. An apparent infrared singularity of this moment is shown to be due to an improper use of perturbation theory, and is removed and replaced with a finite, field-dependent moment, by use of Furry picture propagators

Bounds for Asian basket options

Science.gov (United States)

Deelstra, Griselda; Diallo, Ibrahima; Vanmaele, Michèle

2008-09-01

In this paper we propose pricing bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework. We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151-168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3-33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55-57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51-90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1-52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity.

Infrared divergences of Green functions and renormalization in massless theories. 2

International Nuclear Information System (INIS)

Anikin, S.A.; Zav'yalova, O.I.; Karchev, N.I.

1981-01-01

General theorems are proved concerning the infrared finiteness of Green functions in theories including massless particles. Considerations are based on α-representation of Feynman diagrams. Necessory conditions are considered for proving theorems in the case of diagrams with massive lines. Under certain conditions the contribution of the considered sections into the Feynman amplitude is shown to be free from infrared divergences, but only for those subgraphs which involve all the massive lines and contain all the outer vertexes in one affinity component

Massless scalar field in de Sitter spacetime: unitary quantum time evolution

International Nuclear Information System (INIS)

Cortez, Jerónimo; Blas, Daniel Martín-de; Marugán, Guillermo A Mena; Velhinho, José M

2013-01-01

We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch–Davies vacuum. (paper)

Adaptive Sliding Mode Control of MEMS Gyroscope Based on Neural Network Approximation

Directory of Open Access Journals (Sweden)

Yuzheng Yang

2014-01-01

Full Text Available An adaptive sliding controller using radial basis function (RBF network to approximate the unknown system dynamics microelectromechanical systems (MEMS gyroscope sensor is proposed. Neural controller is proposed to approximate the unknown system model and sliding controller is employed to eliminate the approximation error and attenuate the model uncertainties and external disturbances. Online neural network (NN weight tuning algorithms, including correction terms, are designed based on Lyapunov stability theory, which can guarantee bounded tracking errors as well as bounded NN weights. The tracking error bound can be made arbitrarily small by increasing a certain feedback gain. Numerical simulation for a MEMS angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive neural control scheme and demonstrate the satisfactory tracking performance and robustness.

Combinations of probabilistic and approximate quantum cloning and deleting

International Nuclear Information System (INIS)

Qiu Daowen

2002-01-01

We first construct a probabilistic and approximate quantum cloning machine (PACM) and then clarify the relation between the PACM and other cloning machines. After that, we estimate the global fidelity of the approximate cloning that improves the previous estimation for the deterministic cloning machine; and also derive a bound on the success probability of producing perfect multiple clones. Afterwards, we further establish a more generalized probabilistic and approximate cloning and deleting machine (PACDM) and discuss the connections of the PACDM to some of the existing quantum cloning and deleting machines. Finally the global fidelity and a bound on the success probability of the PACDM are obtained. Summarily, the quantum devices established in this paper improve and also greatly generalize some of the existing machines

Triangle identity and free differential algebra of massless higher spins

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A [AN SSSR, Moscow. Fizicheskij Inst.

1989-09-25

In terms of Berezins's theory of symbols of operators, the integral formulation is suggested for the free differential algebra which gives rise to consistent equations of motion of interacting massless fields of all spins 0{le}s<{infinity} in the frameworks of gravity. In the first nontrivial order of the expansion in powers of curvatures, Frobenius consistency conditions for higher-spin equations of motion are shown to reduce to the simple geometrical fast that there are two ways for splitting any quadrangle in two triangles. To clarify our construction, we illustrate how it works in the simplest case of pure gravity. (orig.).

Approximate symmetries of Hamiltonians

Science.gov (United States)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Bound states in the two-dimension massive quantum electrodynamics (Qed2)

International Nuclear Information System (INIS)

Alves, V.S.; Gomes, M.

1994-01-01

This work studies the fermion-antifermion bound states in the (1+1)D two-dimension massive quantum electrodynamic in the 1/N expansion. The scattering matrices in the non-relativistic approximation have been calculated through TQC, and compared with the cross section in the Born approximation, and therefore the potential responsible by the interactions in the scattering processes have been obtained. Using Schroedinger equation, the existence of possible bound states have been investigated

Approximating the ground state of gapped quantum spin systems

Energy Technology Data Exchange (ETDEWEB)

Michalakis, Spyridon [Los Alamos National Laboratory; Hamza, Eman [NON LANL; Nachtergaele, Bruno [NON LANL; Sims, Robert [NON LANL

2009-01-01

We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Z{sup d}. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset {chi} {contained_in} V the ground state projector can be approximated by the product of two projections, one supported on {chi} and one supported on {chi}{sup c}, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.

Generalized Skyrme model with the loosely bound potential

Science.gov (United States)

Gudnason, Sven Bjarke; Zhang, Baiyang; Ma, Nana

2016-12-01

We study a generalization of the loosely bound Skyrme model which consists of the Skyrme model with a sixth-order derivative term—motivated by its fluidlike properties—and the second-order loosely bound potential—motivated by lowering the classical binding energies of higher-charged Skyrmions. We use the rational map approximation for the Skyrmion of topological charge B =4 , calculate the binding energy of the latter, and estimate the systematic error in using this approximation. In the parameter space that we can explore within the rational map approximation, we find classical binding energies as low as 1.8%, and once taking into account the contribution from spin-isospin quantization, we obtain binding energies as low as 5.3%. We also calculate the contribution from the sixth-order derivative term to the electric charge density and axial coupling.

Fast and reliable method for computing free-bound emission coefficients for hydrogenic ions

Energy Technology Data Exchange (ETDEWEB)

Sarmiento, A; Canto, J

1985-12-01

An approximate formula for the computation of the free-bound emission coefficient for hydrogenic ions is presented. The approximation is obtained through a manipulation of the (free-bound) Gaunt factor which intentionally distinguish the dependence on frequency from the dependence on temperature and ionic composition. Numerical tests indicate that the derived formula is very precise, fast and easy to use, making the calculation of the free-bound contribution from an ionized region of varying temperature and ionic composition a very simple and time-saving task.

Computationally efficient analytic representations of relativistic bound-bound, bound-unbound and unbound-unbound transition matrix elements of hydrogenic atoms

International Nuclear Information System (INIS)

Soldatov, A.; Seke, J.; Adam, G.; Polak, M.

2008-01-01

Full text: A closed analytic form for relativistic transition matrix elements between bound-bound, bound-unbound and unbound-unbound relativistic eigenstates of hydrogenic atoms by using the plane-wave expansion for the electromagnetic-field vector potential was derived in a form convenient for large-scale numerical calculations in QED. By applying the obtained formulae, these transition matrix elements can be evaluated analytically and numerically. These exact matrix elements, which to our knowledge have not been calculated as yet, are of great importance in the analysis of various atom-field interaction processes where retardation effects cannot be ignored. The ultimate goal of the ongoing research is to develop a general universal calculation technique for Seke's approximation and renormalization method in QED, for which the usage of the plane vector expansion for the vector potential is a preferable choice. However, our primary interest lies in the Lamb-shift calculation. Our nearest objective is to carry out the plain-style relativistic calculations of the Lamb shift of the energy levels of hydrogen-like atoms and ions from first principles in the second and higher perturbative orders, using the corresponding convenient as well as novel expressions for the magnitude in question as they stand, i.e. without any additional approximations. Due to that there is no way to achieve all the above-declared goals without recourse to large-scale laborious and time-consuming high-precision numerical calculations, having the transition matrix elements of all possible types in an analytic, convenient for their efficient numerical evaluation form, would be highly advantageous and even unavoidable, especially for calculations of various QED effects in higher perturbative orders be it, equally, in traditional or novel approach. (author)

Three-point Green's function of massless QED in position space to lowest order

International Nuclear Information System (INIS)

Mitra, Indrajit

2009-01-01

The transverse part of the three-point Green's function of massless QED is determined to the lowest order in position space. Taken together with the evaluation of the longitudinal part in Mitra (2008) (J. Phys. A: Math. Theor. 41 315401), this gives a relation for QED which is analogous to the star-triangle relation. We relate our result to conformal-invariant three-point functions

Cubic scattering amplitudes for all massless representations of the Poincare group in any space-time dimension

International Nuclear Information System (INIS)

Fradkin, E.S.; Metsaev, R.R.

1996-02-01

Using the language of highest weight representations and the light cone formalism we construct a full list of cubic amplitudes of scattering for all bosonic massless representations of the Poincare group in any even space-time dimension. (author). 29 refs

A Model-Free No-arbitrage Price Bound for Variance Options

Energy Technology Data Exchange (ETDEWEB)

Bonnans, J. Frederic, E-mail: frederic.bonnans@inria.fr [Ecole Polytechnique, INRIA-Saclay (France); Tan Xiaolu, E-mail: xiaolu.tan@polytechnique.edu [Ecole Polytechnique, CMAP (France)

2013-08-01

We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.

Light-cone gauge versus proper-time gauge for massless spinning particles

International Nuclear Information System (INIS)

Skagerstam, B.S.; Stern, A.

1987-01-01

Although the light-cone gauge is convenient for many applications in physics, it is known to distort topology. We show that as a consequence, some interesting, possibly physical, features of a quantum theory may be missed when working in the light-cone gauge. We shall illustrate this by examining the description of massless spinning particles in an arbitrary number of space-time dimensions. When quantizing such particles in four space-time dimensions (without introducing Grassmann degrees of freedom), the light-cone gauge yields a purely bosonic spectrum, i.e. the helicity λ is integer-valued. The problem is rectified by going to the proper-time gauge; there λ = 0, ±1/2, ±1, ... Upon using the proper-time gauge to quantize massless particle systems in more than four space-time dimensions, we find the following interesting features: Except for space-time dimension d equal to 5 and 9, (i) wave functions cannot be expressed as global functions of momentum (or position). (This is also true for d=4.) Further, for d ≠ 5 and 9, (ii) the helicity group spin (d-2) and (iii) canonical position operators do not exist, globally. (The result that helicity cannot be globally defined resembles a known property of nonabelian monopoles arising in grand unified theories. There, topological obstructions prevent one from defining the color group, globally.) All of the features (i)-(iii) are missed when working in the light-cone gauge. (orig.)

General bounds in Hybrid Natural Inflation

Science.gov (United States)

Germán, Gabriel; Herrera-Aguilar, Alfredo; Hidalgo, Juan Carlos; Sussman, Roberto A.; Tapia, José

2017-12-01

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other, therefore covering the whole range of possible energy scales. In any case the inflationary sector of the model is of the form V(phi)=V0 (1+a cos(phi/f)) where 0waterfall field. One interesting characteristic of this model is that the slow-roll parameter epsilon(phi) is a non-monotonic function of phi presenting a maximum close to the inflection point of the potential. Because the scalar spectrum Script Ps(k) of density fluctuations when written in terms of the potential is inversely proportional to epsilon(phi) we find that Script Ps(k) presents a minimum at phimin. The origin of the HNI potential can be traced to a symmetry breaking phenomenon occurring at some energy scale f which gives rise to a (massless) Goldstone boson. Non-perturbative physics at some temperature Tmodels is not common. We use this property of HNI to determine bounds for the inflationary energy scale Δ and for the tensor-to-scalar ratio r.

Distributed Large Independent Sets in One Round On Bounded-independence Graphs

OpenAIRE

Halldorsson , Magnus M.; Konrad , Christian

2015-01-01

International audience; We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor. Bounded-independence graphs capture various models of wireless networks such as the unit disc graphs model and the quasi unit disc graphs model. For instance, on unit disc graphs, our achieved approximation ratio is O((log(n)/log(log(n)))^2).A starting point of our w...

A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

1999-01-01

The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

Simultaneous dense coding affected by fluctuating massless scalar field

Science.gov (United States)

Huang, Zhiming; Ye, Yiyong; Luo, Darong

2018-04-01

In this paper, we investigate the simultaneous dense coding (SDC) protocol affected by fluctuating massless scalar field. The noisy model of SDC protocol is constructed and the master equation that governs the SDC evolution is deduced. The success probabilities of SDC protocol are discussed for different locking operators under the influence of vacuum fluctuations. We find that the joint success probability is independent of the locking operators, but other success probabilities are not. For quantum Fourier transform and double controlled-NOT operators, the success probabilities drop with increasing two-atom distance, but SWAP operator is not. Unlike the SWAP operator, the success probabilities of Bob and Charlie are different. For different noisy interval values, different locking operators have different robustness to noise.

Free massless fermionic fields of arbitrary spin in d-dimensional anti-de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A

1988-04-25

Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d-2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.

The classical electromagnetic theory which corresponds to the two dimensions quantum electrodynamics with massless fermions

International Nuclear Information System (INIS)

Galvao, C.A.P.; Mignaco, J.A.

1994-01-01

The classical electromagnetic theory is analysed which corresponds to the two-dimensional quantum electrodynamics with massless spinor fields (Schwinger model). The chiral anomaly is introduced as a currents property, which in the two-dimensional spinor fields are duality related. It is also shown that the resulting classical theory is consistent. (author). 5 refs

Spectral computations for bounded operators

CERN Document Server

Ahues, Mario; Limaye, Balmohan

2001-01-01

Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for research scientists, Spectral Computations for Bounded Operators addresses the issue of solving eigenvalue problems for operators on infinite dimensional spaces. From a review of classical spectral theory through concrete approximation techniques to finite dimensional situations that can be implemented on a computer, this volume illustrates the marriage of pure and applied mathematics. It contains a variety of recent developments, including a new type of approximation that encompasses a variety of approximation methods but is simple to verify in practice. It also suggests a new stopping criterion for the QR Method and outlines advances in both the iterative refineme...

Free massless fields of arbitrary spin in the de Sitter space and initial data for a higher spin superalgebra

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A

1987-11-01

Linearized curvatures are constructed for massless higher spin fields on the (anti-) de Sitter background. The quite uniform description for free massless fields of all integer and half-integer spins s greater than or equal to 3/2 is presented, based on these curvatures. In particular, the actions and the equations of motion are given in a simple form. The proposed linearized curvatures provide 'initial data' for determination of a non-Abelian higher spin symmetry that may correspond to a hypothetical non-trivial theory of higher spins interacting with gravity and themselves. It is noted that the conjugation law for fermion fields should be modified drastically after transition from the anti-de-Sitter geometry to the de Sitter one.

Testing and using the Lewin-Lieb bounds in density functional theory

Science.gov (United States)

Feinblum, David; Kenison, John; Burke, Kieron

Lewin and Lieb have recently proven several new bounds on the exchange-correlation energy that complement the Lieb-Oxford bound. We test these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding them usually less strict than the Lieb-Oxford bound. However, we also show that, if a generalized gradient approximation (GGA) is to guarantee satisfaction of the new bounds for all densities, new restrictions on the the exchange-correlation enhancement factor are implied. We thank Mathieu Lewin and Elliott Lieb for bringing their new bounds to our attention, and Eberhard Engel for developing the OPMKS atom code. This work was supported by NSF under Grant CHE-1112442.

Polynomial approximation of functions in Sobolev spaces

International Nuclear Information System (INIS)

Dupont, T.; Scott, R.

1980-01-01

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces

A fast and reliable method for computing free-bound emission coefficients for hydrogenic ions

International Nuclear Information System (INIS)

Sarmiento, A.; Canto, J.

1985-01-01

An approximate formula for the computation of the free-bound emission coefficient for hydrogenic ions is presented. The approximation is obtained through a manipulation of the (free-bound) Gaunt factor which intentionally distinguish the dependence on frequency from the dependence on temperature and ionic composition. Numerical tests indicate that the derived formula is very precise, fast and easy to use, making the calculation of the free-bound contribution from an ionized region of varying temperature and ionic composition a very simple and time-saving task. (author)

An improved nonparametric lower bound of species richness via a modified good-turing frequency formula.

Science.gov (United States)

Chiu, Chun-Huo; Wang, Yi-Ting; Walther, Bruno A; Chao, Anne

2014-09-01

It is difficult to accurately estimate species richness if there are many almost undetectable species in a hyper-diverse community. Practically, an accurate lower bound for species richness is preferable to an inaccurate point estimator. The traditional nonparametric lower bound developed by Chao (1984, Scandinavian Journal of Statistics 11, 265-270) for individual-based abundance data uses only the information on the rarest species (the numbers of singletons and doubletons) to estimate the number of undetected species in samples. Applying a modified Good-Turing frequency formula, we derive an approximate formula for the first-order bias of this traditional lower bound. The approximate bias is estimated by using additional information (namely, the numbers of tripletons and quadrupletons). This approximate bias can be corrected, and an improved lower bound is thus obtained. The proposed lower bound is nonparametric in the sense that it is universally valid for any species abundance distribution. A similar type of improved lower bound can be derived for incidence data. We test our proposed lower bounds on simulated data sets generated from various species abundance models. Simulation results show that the proposed lower bounds always reduce bias over the traditional lower bounds and improve accuracy (as measured by mean squared error) when the heterogeneity of species abundances is relatively high. We also apply the proposed new lower bounds to real data for illustration and for comparisons with previously developed estimators. © 2014, The International Biometric Society.

Recursive B-spline approximation using the Kalman filter

Directory of Open Access Journals (Sweden)

Jens Jauch

2017-02-01

Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.

Geometric convergence of some two-point Pade approximations

International Nuclear Information System (INIS)

Nemeth, G.

1983-01-01

The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)

Perturbation of operators and approximation of spectrum

Indian Academy of Sciences (India)

outside the bounds of essential spectrum of A(x) can be approximated ... some perturbed discrete Schrödinger operators treating them as block ...... particular, one may think of estimating the spectrum and spectral gaps of Schrödinger.

An Approximate Approach to Automatic Kernel Selection.

Science.gov (United States)

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Geometric representation of the generator of duality in massless and massive p-form field theories

International Nuclear Information System (INIS)

Contreras, Ernesto; Martinez, Yisely; Leal, Lorenzo

2010-01-01

We study the invariance under duality transformations in massless and massive p-form field theories and obtain the Noether generators of the infinitesimal transformations that correspond to this symmetry. These generators can be realized in geometrical representations that generalize the loop representation of the Maxwell field, allowing for a geometrical interpretation which is studied.

Regulating the infrared by mode matching: a massless scalar in expanding spaces with constant deceleration

NARCIS (Netherlands)

Janssen, T.M.; Prokopec, T.

2011-01-01

In this paper we consider a massless scalar field, with a possible coupling ξ to the Ricci scalar in a D dimensional Friedmann-Lemaître-Robertson-Walker space-time with a constant deceleration parameter q=ϵ-1, ϵ=-H˙/H2. Correlation functions for the Bunch-Davies vacuum of such a theory have long

Universal bounds in even-spin CFTs

Energy Technology Data Exchange (ETDEWEB)

Qualls, Joshua D. [Department of Physics, National Taiwan University,Taipei, Taiwan (China)

2015-12-01

We prove using invariance under the modular S− and ST−transformations that every unitary two-dimensional conformal field theory (CFT) having only even-spin primary operators (with no extended chiral algebra and with right- and left-central charges c,c̃>1) contains a primary operator with dimension Δ{sub 1} satisfying 0<Δ{sub 1}<((c+c̃)/24)+0.09280…. After deriving both analytical and numerical bounds, we discuss how to extend our methods to bound higher conformal dimensions before deriving lower and upper bounds on the number of primary operators in a given energy range. Using the AdS{sub 3}/CFT{sub 2} dictionary, the bound on Δ{sub 1} proves the lightest massive excitation in appropriate theories of 3D matter and gravity with cosmological constant Λ<0 can be no heavier than 1/8G{sub N}+O(√(−Λ)); the bounds on the number of operators are related via AdS/CFT to the entropy of states in the dual gravitational theory. In the flat-space approximation, the limiting mass is exactly that of the lightest BTZ black hole.

Resolvent-based modeling of passive scalar dynamics in wall-bounded turbulence

Science.gov (United States)

Dawson, Scott; Saxton-Fox, Theresa; McKeon, Beverley

2017-11-01

The resolvent formulation of the Navier-Stokes equations expresses the system state as the output of a linear (resolvent) operator acting upon a nonlinear forcing. Previous studies have demonstrated that a low-rank approximation of this linear operator predicts many known features of incompressible wall-bounded turbulence. In this work, this resolvent model for wall-bounded turbulence is extended to include a passive scalar field. This formulation allows for a number of additional simplifications that reduce model complexity. Firstly, it is shown that the effect of changing scalar diffusivity can be approximated through a transformation of spatial wavenumbers and temporal frequencies. Secondly, passive scalar dynamics may be studied through the low-rank approximation of a passive scalar resolvent operator, which is decoupled from velocity response modes. Thirdly, this passive scalar resolvent operator is amenable to approximation by semi-analytic methods. We investigate the extent to which this resulting hierarchy of models can describe and predict passive scalar dynamics and statistics in wall-bounded turbulence. The support of AFOSR under Grant Numbers FA9550-16-1-0232 and FA9550-16-1-0361 is gratefully acknowledged.

Infrared behaviour of massless QED in space-time dimensions 2

International Nuclear Information System (INIS)

Mitra, Indrajit; Ratabole, Raghunath; Sharatchandra, H.S.

2005-01-01

We show that the logarithmic infrared divergences in electron self-energy and vertex function of massless QED in 2+1 dimensions can be removed at all orders of 1/N by an appropriate choice of a non-local gauge. Thus the infrared behaviour given by the leading order in 1/N is not modified by higher order corrections. Our analysis gives a computational scheme for the Amati-Testa model, resulting in a non-trivial conformal invariant field theory for all space-time dimensions 2< d<4

Infrared behaviour of massless QED in space-time dimensions 2

Energy Technology Data Exchange (ETDEWEB)

Mitra, Indrajit [The Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India) and Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan-Nagar, Kolkata 700064 (India)]. E-mail: indra@theory.saha.ernet.in; Ratabole, Raghunath [The Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India)]. E-mail: raghu@imsc.res.in; Sharatchandra, H.S. [The Institute of Mathematical Sciences, C.I.T. Campus, Taramani P.O., Chennai 600113 (India)]. E-mail: sharat@imsc.res.in

2005-04-07

We show that the logarithmic infrared divergences in electron self-energy and vertex function of massless QED in 2+1 dimensions can be removed at all orders of 1/N by an appropriate choice of a non-local gauge. Thus the infrared behaviour given by the leading order in 1/N is not modified by higher order corrections. Our analysis gives a computational scheme for the Amati-Testa model, resulting in a non-trivial conformal invariant field theory for all space-time dimensions 2

Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap

International Nuclear Information System (INIS)

Cichy, Krzysztof; Poznan Univ.; Kujawa-Cichy, Agnieszka; Szyniszewski, Marcin; Manchester Univ.

2012-12-01

We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10 -6 %.

Axial gravity, massless fermions and trace anomalies

International Nuclear Information System (INIS)

Bonora, L.; Cvitan, M.; Giaccari, S.; Stemberga, T.; Prester, P.D.; Pereira, A.D.; UFF-Univ. Federal Fluminense, Niteroi

2017-01-01

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)

Axial gravity, massless fermions and trace anomalies

Energy Technology Data Exchange (ETDEWEB)

Bonora, L. [International School for Advanced Studies (SISSA), Trieste (Italy); KEK, Tsukuba (Japan). KEK Theory Center; INFN, Sezione di Trieste (Italy); Cvitan, M.; Giaccari, S.; Stemberga, T. [Zagreb Univ. (Croatia). Dept. of Physics; Prester, P.D. [Rijeka Univ. (Croatia). Dept. of Physics; Pereira, A.D. [UERJ-Univ. Estadual do Rio de Janeiro (Brazil). Dept. de Fisica Teorica; UFF-Univ. Federal Fluminense, Niteroi (Brazil). Inst. de Fisica

2017-08-15

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones. (orig.)

Veselago focusing of anisotropic massless Dirac fermions

Science.gov (United States)

Zhang, Shu-Hui; Yang, Wen; Peeters, F. M.

2018-05-01

Massless Dirac fermions (MDFs) emerge as quasiparticles in various novel materials such as graphene and topological insulators, and they exhibit several intriguing properties, of which Veselago focusing is an outstanding example with a lot of possible applications. However, up to now Veselago focusing merely occurred in p-n junction devices based on the isotropic MDF, which lacks the tunability needed for realistic applications. Here, motivated by the emergence of novel Dirac materials, we investigate the propagation behaviors of anisotropic MDFs in such a p-n junction structure. By projecting the Hamiltonian of the anisotropic MDF to that of the isotropic MDF and deriving an exact analytical expression for the propagator, precise Veselago focusing is demonstrated without the need for mirror symmetry of the electron source and its focusing image. We show a tunable focusing position that can be used in a device to probe masked atom-scale defects. This study provides an innovative concept to realize Veselago focusing relevant for potential applications, and it paves the way for the design of novel electron optics devices by exploiting the anisotropic MDF.

Capacity bounds for kth best path selection over generalized fading channels

KAUST Repository

Hanif, Muhammad Fainan

2014-02-01

Exact ergodic capacity calculation for fading wireless channels typically involves time-consuming numerical evaluation of infinite integrals. In this paper, lower and upper bounds on ergodic capacity for kth best path are presented. These bounds have simple analytic expressions which allow their fast evaluation. Numerical results show that the newly proposed bounds closely approximate the exact ergodic capacity for a large variety of system configurations. © 1997-2012 IEEE.

An analytic distribution function for a mass-less cored stellar system in a cuspy dark-matter halo

NARCIS (Netherlands)

Breddels, Maarten A.; Helmi, Amina

2013-01-01

We demonstrate the existence of a distribution function that can be used to represent spherical mass-less cored stellar systems having constant mildly tangential velocity anisotropy embedded in cuspy dark-matter halos. In particular, we derived analytically the functional form of the distribution

2D massless QED Hall half-integer conductivity and graphene

International Nuclear Information System (INIS)

Martínez, A Pérez; Querts, E Rodriguez; Rojas, H Pérez; Gaitan, R; Rodriguez-Romo, S

2011-01-01

Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system C-non-invariant under fermion–antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature, the main features of the quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to e 2 /h for the Hall conductivity. For typical values of graphene the plateaus of the Hall conductivity are also reproduced. (paper)

Approximation methods in loop quantum cosmology: from Gowdy cosmologies to inhomogeneous models in Friedmann–Robertson–Walker geometries

International Nuclear Information System (INIS)

Martín-Benito, Mercedes; Martín-de Blas, Daniel; Marugán, Guillermo A Mena

2014-01-01

We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann–Robertson–Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions. (paper)

A non-perturbative approach to the Coleman-Weinberg mechanism in massless scalar QED

International Nuclear Information System (INIS)

Malbouisson, A.P.C.; Nogueira, F.S.; Svaiter, N.F.

1995-08-01

We rederived non-perturbatively the Coleman-Weinberg expression for the effective potential for massless scalar QED. Our result is not restricted to small values of the coupling constants. This shows that the Coleman-Weinberg result can be established beyond the range of perturbation theory. Also, we derive it in a manifestly renormalization group invariant way. It is shown that with the derivation given no Landau ghost singularity arises. The finite temperature case is discussed. (author). 13 refs

Bounds on the performance of a class of digital communication systems

Science.gov (United States)

Polk, D. R.; Gupta, S. C.; Cohn, D. L.

1973-01-01

Bounds on the capacity of a class of digital communication channels are derived. Equating the bounds on capacity to rate-distortion functions of (typical) sources in turn produces bounds on the performance of a class of digital communication systems. For ratios of squared quantization level to noise variance much less than one, the power requirements for this class of digital communication systems are shown to be within approximately 3 dB of the theoretical optimum.

Finite Element Approximation of the FENE-P Model

OpenAIRE

Barrett , John ,; Boyaval , Sébastien

2017-01-01

We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\\subset$ R d , d = 2 or 3$, subject to no flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conforma-tion tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a) the velocity field is approximated by c...

Lattice Hamiltonian approach to the massless Schwinger model. Precise extraction of the mass gap

Energy Technology Data Exchange (ETDEWEB)

Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Kujawa-Cichy, Agnieszka [Poznan Univ. (Poland). Faculty of Physics; Szyniszewski, Marcin [Poznan Univ. (Poland). Faculty of Physics; Manchester Univ. (United Kingdom). NOWNano DTC

2012-12-15

We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10{sup -6} %.

Hardness of approximation for strip packing

DEFF Research Database (Denmark)

Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin

2017-01-01

Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively......)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two...

Approximate solutions of the Wei Hua oscillator using the Pekeris ...

Indian Academy of Sciences (India)

The approximate analytical bound-state solutions of the Schrödinger equation for the. Wei Hua oscillator are carried out in N-dimensional space by taking Pekeris approximation scheme to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov ...

Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients

CERN Document Server

Hutzenthaler, Martin

2015-01-01

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation method

Topological Symmetry, Spin Liquids and CFT Duals of Polyakov Model with Massless Fermions

Energy Technology Data Exchange (ETDEWEB)

Unsal, Mithat

2008-04-30

We prove the absence of a mass gap and confinement in the Polyakov model with massless complex fermions in any representation of the gauge group. A U(1){sub *} topological shift symmetry protects the masslessness of one dual photon. This symmetry emerges in the IR as a consequence of the Callias index theorem and abelian duality. For matter in the fundamental representation, the infrared limits of this class of theories interpolate between weakly and strongly coupled conformal field theory (CFT) depending on the number of flavors, and provide an infinite class of CFTs in d = 3 dimensions. The long distance physics of the model is same as certain stable spin liquids. Altering the topology of the adjoint Higgs field by turning it into a compact scalar does not change the long distance dynamics in perturbation theory, however, non-perturbative effects lead to a mass gap for the gauge fluctuations. This provides conceptual clarity to many subtle issues about compact QED{sub 3} discussed in the context of quantum magnets, spin liquids and phase fluctuation models in cuprate superconductors. These constructions also provide new insights into zero temperature gauge theory dynamics on R{sup 2,1} and R{sup 2,1} x S{sup 1}. The confined versus deconfined long distance dynamics is characterized by a discrete versus continuous topological symmetry.

Relativistic bound-state problem of a one-dimensional system

International Nuclear Information System (INIS)

Sato, T.; Niwa, T.; Ohtsubo, H.; Tamura, K.

1991-01-01

A Poincare-covariant description of the two-body bound-state problem in one-dimensional space is studied by using the relativistic Schrodinger equation. We derive the many-body Hamiltonian, electromagnetic current and generators of the Poincare group in the framework of one-boson exchange. Our theory satisfies Poincare algebra within the one-boson-exchange approximation. We numerically study the relativistic effects on the bound-state wavefunction and the elastic electromagnetic form factor. The Lorentz boost of the bound-state wavefunction and the two-body exchange current are shown to play an important role in guaranteeing the Lorentz invariance of the form factor. (author)

A 1.375-approximation algorithm for sorting by transpositions.

Science.gov (United States)

Elias, Isaac; Hartman, Tzvika

2006-01-01

Sorting permutations by transpositions is an important problem in genome rearrangements. A transposition is a rearrangement operation in which a segment is cut out of the permutation and pasted in a different location. The complexity of this problem is still open and it has been a 10-year-old open problem to improve the best known 1.5-approximation algorithm. In this paper, we provide a 1.375-approximation algorithm for sorting by transpositions. The algorithm is based on a new upper bound on the diameter of 3-permutations. In addition, we present some new results regarding the transposition diameter: we improve the lower bound for the transposition diameter of the symmetric group and determine the exact transposition diameter of simple permutations.

Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC

KAUST Repository

Shakir, Muhammad; Durrani, Tariq S; Alouini, Mohamed-Slim

2011-01-01

demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity

Relativistic gravitation from massless systems of scalar and vector fields

International Nuclear Information System (INIS)

Fonseca Teixeira, A.F. da.

1979-01-01

Under the laws of Einstein's gravitational theory, a massless system consisting of the diffuse sources of two fields is discussed. One fields is scalar, of long range, the other is a vector field of short range. A proportionality between the sources is assumed. Both fields are minimally coupled to gravitation, and contribute positive definitely to the time component of the energy momentum tensor. A class of static, spherically symmetric solutions of the equations is obtained, in the weak field limit. The solutions are regular everywhere, stable, and can represent large or small physical systems. The gravitational field presents a Schwarzschild-type asymptotic behavior. The dependence of the energy on the various parameters characterizing the system is discussed in some detail. (Author) [pt

On the consistent interactions in D=11 among a graviton, a massless gravitino and a three-form

International Nuclear Information System (INIS)

Cioroianu, E.M.; Diaconu, E.; Sararu, S.C.

2009-01-01

The couplings that can be introduced between a massless Rarita-Schwinger field, a Pauli-Fierz field and an Abelian three-form gauge field in eleven spacetime dimensions are analyzed in the context of the deformation of the solution of the master equation. (Abstract Copyright [2009], Wiley Periodicals, Inc.)

A bound for the convergence rate of parallel tempering for sampling restricted Boltzmann machines

DEFF Research Database (Denmark)

Fischer, Asja; Igel, Christian

2015-01-01

on sampling. Parallel tempering (PT), an MCMC method that maintains several replicas of the original chain at higher temperatures, has been successfully applied for RBM training. We present the first analysis of the convergence rate of PT for sampling from binary RBMs. The resulting bound on the rate...... of convergence of the PT Markov chain shows an exponential dependency on the size of one layer and the absolute values of the RBM parameters. It is minimized by a uniform spacing of the inverse temperatures, which is often used in practice. Similarly as in the derivation of bounds on the approximation error...... for contrastive divergence learning, our bound on the mixing time implies an upper bound on the error of the gradient approximation when the method is used for RBM training....

Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton

Energy Technology Data Exchange (ETDEWEB)

Vecchia, Paolo Di [The Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark); Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden); Marotta, Raffaele [Istituto Nazionale di Fisica Nucleare, Sezione di Napoli,Complesso Universitario di Monte S. Angelo ed. 6, via Cintia, 80126, Napoli (Italy); Mojaza, Matin [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam (Germany)

2016-12-06

We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz) massless sector of closed superstrings in the case where one external state becomes soft. We compute the amplitudes generically for any number of dimensions and any number and kind of the massless closed states through the subsubleading order in the soft expansion. We show that, when the soft state is a graviton or a dilaton, the full result can be expressed as a soft theorem factorizing the amplitude in a soft and a hard part. This behavior is similar to what has previously been observed in field theory and in the bosonic string. Differently from the bosonic string, the supersymmetric soft theorem for the graviton has no string corrections at subsubleading order. The dilaton soft theorem, on the other hand, is found to be universally free of string corrections in any string theory.

Soft behavior of a closed massless state in superstring and universality of the soft behavior of the dilaton

DEFF Research Database (Denmark)

di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin

2016-01-01

We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz) massless sector of closed superstrings in the case where one external state becomes soft. We compute the amplitudes generically for any number of dimensions and any number and kind of the massless closed states through...... the subsubleading order in the soft expansion. We show that, when the soft state is a graviton or a dilaton, the full result can be expressed as a soft theorem factorizing the amplitude in a soft and a hard part. This behavior is similar to what has previously been observed in field theory and in the bosonic string....... Differently from the bosonic string, the supersymmetric soft theorem for the graviton has no string corrections at subsubleading order. The dilaton soft theorem, on the other hand, is found to be universally free of string corrections in any string theory....

Efficient Approximation of Optimal Control for Markov Games

DEFF Research Database (Denmark)

Fearnley, John; Rabe, Markus; Schewe, Sven

2011-01-01

We study the time-bounded reachability problem for continuous-time Markov decision processes (CTMDPs) and games (CTMGs). Existing techniques for this problem use discretisation techniques to break time into discrete intervals, and optimal control is approximated for each interval separately...

The adiabatic approximation in multichannel scattering

International Nuclear Information System (INIS)

Schulte, A.M.

1978-01-01

Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)

The approximation gap for the metric facility location problem is not yet closed

NARCIS (Netherlands)

Byrka, J.; Aardal, K.I.

2007-01-01

We consider the 1.52-approximation algorithm of Mahdian et al. for the metric uncapacitated facility location problem. We show that their algorithm does not close the gap with the lower bound on approximability, 1.463, by providing a construction of instances for which its approximation ratio is not

A simple approximation to the bivariate normal distribution with large correlation coefficient

NARCIS (Netherlands)

Albers, Willem/Wim; Kallenberg, W.C.M.

1994-01-01

The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the

Green's functions for theories with massless particles (in perturbation theory). [Growth properties, momentum space, mass renormalization

Energy Technology Data Exchange (ETDEWEB)

Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)

1975-01-01

With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.

OPRA capacity bounds for selection diversity over generalized fading channels

KAUST Repository

Hanif, Muhammad Fainan

2014-05-01

Channel side information at the transmitter can increase the average capacity by enabling optimal power and rate adaptation. The resulting optimal power and rate adaptation (OPRA) capacity rarely has a closed-form analytic expression. In this paper, lower and upper bounds on OPRA capacity for selection diversity scheme are presented. These bounds hold for variety of fading channels including log-normal and generalized Gamma distributed models and have very simple analytic expressions for easy evaluation even for kth best path selection. Some selected numerical results show that the newly proposed bounds closely approximate the actual OPRA capacity. © 2014 IEEE.

A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

KAUST Repository

Fowkes, Jaroslav M.

2012-06-21

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations. © 2012 Springer Science+Business Media, LLC.

Upper Bounds on Performance Measures of Heterogeneous // Queues

Directory of Open Access Journals (Sweden)

F. S. Q. Alves

2011-01-01

Full Text Available In many real-life queueing systems, the servers are often heterogeneous, namely they work at different rates. This paper provides a simple method to compute tight upper bounds on two important performance measures of single-class heterogeneous multi-server Markovian queueing systems, namely the average number in queue and the average waiting time in queue. This method is based on an expansion of the state space that is followed by an approximate reduction of the state space, only considering the most probable states. In most cases tested, we were able to approximate the actual behavior of the system with smaller errors than those obtained from traditional homogeneous multiserver Markovian queues, as shown by GPSS simulations. In addition, we have correlated the quality of the approximation with the degree of heterogeneity of the system, which was evaluated using its Gini index. Finally, we have shown that the bounds are robust and still useful, even considering quite different allocation strategies. A large number of simulation results show the accuracy of the proposed method that is better than that of classical homogeneous multiserver Markovian formulae in many situations.

Two-vibron bound states in the β–Fermi–Pasta–Ulam model

International Nuclear Information System (INIS)

Hu Xinguang; Tang Yi

2008-01-01

This paper studies the two-vibron bound states in the β–Fermi–Pasta–Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems. (condensed matter: structure, thermal and mechanical properties)

Estimating the Effective Lower Bound for the Czech National Bank's Policy Rate

OpenAIRE

Kolcunova, Dominika; Havranek, Tomas

2018-01-01

The paper focuses on the estimation of the effective lower bound for the Czech National Bank's policy rate. The effective lower bound is determined by the value below which holding and using cash would be more convenient than deposits with negative yields. This bound is approximated based on storage, the insurance and transportation costs of cash and the costs associated with the loss of the convenience of cashless payments and complemented with the estimate based on interest charges, which p...

Scattering of massless lumps and non-local charges in the two-dimensional classical non-linear sigma-model

International Nuclear Information System (INIS)

Luescher, M.; Pohlmeyer, K.

1977-09-01

Finite energy solutions of the field equations of the non-linear sigma-model are shown to decay asymptotically into massless lumps. By means of a linear eigenvalue problem connected with the field equations we then find an infinite set of dynamical conserved charges. They, however, do not provide sufficient information to decode the complicated scattering of lumps. (orig.) [de

Thermodynamics of lattice QCD with massless quarks and chiral 4-fermion interactions

International Nuclear Information System (INIS)

Kogut, J. B.

1998-01-01

N f = 2 lattice QCD with massless quarks and a weak 4-fermion interaction appears to have the expected second order transition, at least for N t ≥ 6. More work is needed to clarify the N t = 4 case. With more statistics the N t = 6 simulations should produce an accurate determination of the critical exponent β m . Moving to finite mass at β = β c should allow an accurate determination of σ. Hadronic screening masses need further analysis. Other order parameters remain to be analyzed. Unfortunately, there is no obvious way to include 4-fermion interactions with full SU(2) x SU(2) chiral flavor symmetry

The scalar-photon 3-point vertex in massless quenched scalar QED

International Nuclear Information System (INIS)

Concha-Sánchez, Y; Gutiérrez-Guerrero, L X; Fernández-Rangel, L A

2016-01-01

Non perturbative studies of Schwinger-Dyson equations (SDEs) require their infinite, coupled tower to be truncated in order to reduce them to a practically solvable set. In this connection, a physically acceptable ansatz for the three point vertex is the most favorite choice. Scalar quantum electrodynamics (sQED) provides a simple and neat platform to address this problem. The most general form of the scalar-photon three point vertex can be expressed in terms of only two independent form factors, longitudinal and transverse. Ball and Chiu have demonstrated that the longitudinal vertex is fixed by requiring the Ward-Fradkin-Green- Takahashi identity (WFGTI), while the transverse vertex remains undetermined. In massless quenched sQED, we propose the transverse part of the non perturbative scalar-photon vertex. (paper)

No parity anomaly in massless QED3: A BPHZL approach

International Nuclear Information System (INIS)

Del Cima, O.M.; Franco, D.H.T.; Piguet, O.; Schweda, M.

2009-01-01

In this Letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED 3 frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein-Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern-Simons term is generated at that order induced through the infrared subtractions - which violate parity. We show then that, what is called 'parity anomaly', is in fact a parity-odd counterterm needed for restauring parity.

Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

Science.gov (United States)

Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

2018-03-01

The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

Generalized surface tension bounds in vacuum decay

Science.gov (United States)

Masoumi, Ali; Paban, Sonia; Weinberg, Erick J.

2018-02-01

Coleman and De Luccia (CDL) showed that gravitational effects can prevent the decay by bubble nucleation of a Minkowski or AdS false vacuum. In their thin-wall approximation this happens whenever the surface tension in the bubble wall exceeds an upper bound proportional to the difference of the square roots of the true and false vacuum energy densities. Recently it was shown that there is another type of thin-wall regime that differs from that of CDL in that the radius of curvature grows substantially as one moves through the wall. Not only does the CDL derivation of the bound fail in this case, but also its very formulation becomes ambiguous because the surface tension is not well defined. We propose a definition of the surface tension and show that it obeys a bound similar in form to that of the CDL case. We then show that both thin-wall bounds are special cases of a more general bound that is satisfied for all bounce solutions with Minkowski or AdS false vacua. We discuss the limit where the parameters of the theory attain critical values and the bound is saturated. The bounce solution then disappears and a static planar domain wall solution appears in its stead. The scalar field potential then is of the form expected in supergravity, but this is only guaranteed along the trajectory in field space traced out by the bounce.

Perturbation expansions generated by an approximate propagator

International Nuclear Information System (INIS)

Znojil, M.

1987-01-01

Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example

Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC

KAUST Repository

Shakir, Muhammad

2011-09-01

This article presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs). This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading matrix G and the channel path gain matrix Ω. This article demonstrates that the actual capacity converges to the theoretical upper bound under the constraints like low signal-to-noise ratios and limiting channel path gain among the MTs and the respective base station of interest. In order to determine the usefulness of the HUB, the behavior of the theoretical upper bound is critically observed specially when the inter-cell and the intra-cell time sharing schemes are employed. In this context, we derive an analytical form of HUB by employing an approximation approach based on the estimation of probability density function of trace of Hadamard product of two matrices, i.e., G and Ω. A closed form of expression has been derived to capture the effect of the MT distribution on the optimum joint decoding capacity of C-GCMAC. This article demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity of Wyner GCMAC.

Analytical upper bound on optimum joint decoding capacity of Wyner GCMAC using hadamard inequality

KAUST Repository

Shakir, Muhammad

2011-11-01

This paper presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs) across the cells. This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading and channel path gain matrices. In this context, we employ an approximation approach based on the estimation of probability density function (PDF) of Hadamard product of two matrices. A closed-form expression has been derived to capture the effect of variable user density in adjacent cells on optimal joint decoding capacity. The results of this paper demonstrate that the analytical HUB based on the proposed approximation approach converges to the theoretical results for medium range of signal to noise ratios and shows a comparable tighter bound on optimum joint decoding capacity. © 2011 IEEE.

Bound states in weakly disordered spin ladders

Energy Technology Data Exchange (ETDEWEB)

Arlego, M. [Departamento de Fisica, Universidad Nacional de La Plata, CC 67 (1900) La Plata (Argentina)]. E-mail: arlego@venus.fisica.unlp.edu.ar; Brenig, W. [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig (Germany); Cabra, D.C. [Laboratoire de Physique Theorique, Universite Louis Pasteur Strasbourg (France); Heidrich-Meisner, F. [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig (Germany); Honecker, A. [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig (Germany); Rossini, G. [Departamento de Fisica, Universidad Nacional de La Plata, CC 67 (1900) La Plata (Argentina)

2005-04-30

We study the appearance of bound states in the spin gap of spin-12 ladders induced by weak bond disorder. Starting from the strong-coupling limit, i.e., the limit of weakly coupled dimers, we perform a projection on the single-triplet subspace and derive the position of bound states for the single impurity problem of one modified coupling as well as for small impurity clusters. The case of a finite concentration of impurities is treated with the coherent-potential approximation (CPA) in the strong-coupling limit and compared with numerical results. Further, we analyze the details in the structure of the density of states and relate their origin to the influence of impurity clusters.

Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem

KAUST Repository

Lellmann, Jan

2012-11-09

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation methods for finite-dimensional problems. While for the latter several optimality bounds are known, to our knowledge no such bounds exist in the infinite-dimensional setting. We provide such a bound by analyzing a probabilistic rounding method, showing that it is possible to obtain an integral solution of the original partitioning problem from a solution of the relaxed problem with an a priori upper bound on the objective. The approach has a natural interpretation as an approximate, multiclass variant of the celebrated coarea formula. © 2012 Springer Science+Business Media New York.

Closed form bound-state perturbation theory

Directory of Open Access Journals (Sweden)

Ollie J. Rose

1980-01-01

Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.

Two-nucleon bound states in quenched lattice QCD

International Nuclear Information System (INIS)

Yamazaki, T.; Kuramashi, Y.; Ukawa, A.

2011-01-01

We address the issue of bound state in the two-nucleon system in lattice QCD. Our study is made in the quenched approximation at the lattice spacing of a=0.128 fm with a heavy quark mass corresponding to m π =0.8 GeV. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the ground state and the free two-nucleon state by changing the spatial extent of the lattice from 3.1 fm to 12.3 fm. A finite energy difference left in the infinite spatial volume limit leads us to the conclusion that the measured ground states for not only spin triplet but also singlet channels are bounded. Furthermore the existence of the bound state is confirmed by investigating the properties of the energy for the first excited state obtained by a 2x2 diagonalization method. The scattering lengths for both channels are evaluated by applying the finite volume formula derived by Luescher to the energy of the first excited states.

Beyond the small-angle approximation for MBR anisotropy from seeds

International Nuclear Information System (INIS)

Stebbins, A.; Veeraraghavan, S.

1995-01-01

In this paper we give a general expression for the energy shift of massless particles traveling through the gravitational field of an arbitrary matter distribution as calculated in the weak field limit in an asymptotically flat space-time. It is not assumed that matter is nonrelativistic. We demonstrate the surprising result that if the matter is illuminated by a uniform brightness background that the brightness pattern observed at a given point in space-time (modulo a term dependent on the observer's velocity) depends only on the matter distribution on the observer's past light cone. These results apply directly to the cosmological MBR anisotropy pattern generated in the immediate vicinity of an object such as a cosmic string or global texture. We apply these results to cosmic strings, finding a correction to previously published results in the small-angle approximation. We also derive the full-sky anisotropy pattern of a collapsing texture knot

Subquadratic medial-axis approximation in $\\mathbb{R}^3$

Directory of Open Access Journals (Sweden)

Christian Scheffer

2015-09-01

Full Text Available We present an algorithm that approximates the medial axis of a smooth manifold in $\\mathbb{R}^3$ which is given by a sufficiently dense point sample. The resulting, non-discrete approximation is shown to converge to the medial axis as the sampling density approaches infinity. While all previous algorithms guaranteeing convergence have a running time quadratic in the size $n$ of the point sample, we achieve a running time of at most $\\mathcal{O}(n\\log^3 n$. While there is no subquadratic upper bound on the output complexity of previous algorithms for non-discrete medial axis approximation, the output of our algorithm is guaranteed to be of linear size.

Trace anomaly of the stress-energy tensor for massless vector particles propagating in a general background metric

International Nuclear Information System (INIS)

Adler, S.L.; Lieberman, J.

1978-01-01

We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, point out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods

Approximate controllability of the Navier-Stokes system in unbounded domains

International Nuclear Information System (INIS)

Shorygin, P O

2003-01-01

The question of the approximate controllability for the 2- and the 3-dimensional Navier-Stokes system defined in the exterior of a bounded domain ω or in the entire space is studied. It is shown that one can find boundary controls or locally distributed controls (having support in a prescribed bounded domain) defined on the right-hand side of the system such that in prescribed time the solution of the Navier-Stokes system becomes arbitrarily close to an arbitrary prescribed divergence-free vector field

Approximate Receding Horizon Approach for Markov Decision Processes: Average Award Case

National Research Council Canada - National Science Library

Chang, Hyeong S; Marcus, Steven I

2002-01-01

...) with countable state space, finite action space, and bounded rewards that uses an approximate solution of a fixed finite-horizon sub-MDP of a given infinite-horizon MDP to create a stationary policy...

Multilevel weighted least squares polynomial approximation

KAUST Repository

Haji-Ali, Abdul-Lateef

2017-06-30

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

A cluster expansion for bound three-alpha particles as a three-body problem

International Nuclear Information System (INIS)

Osman, A.

1981-08-01

A three-body model is proposed to study the nuclear bound states. The nucleus is described as a bound state of three clusters. A cluster expansion is introduced for the three cluster bound state problem. The present integral equations are treated by simple approximate solutions, which lead to effective potentials by using the present cluster expansion. The 12 C nucleus is described as a three-alpha particle bound state. The binding energy of 12 C is calculated numerically using the present cluster expansion as bound three-alpha clusters. The present three-body cluster expansion calculations are very near to the exact three-body calculations using separable potentials. The present theoretical calculations are in good agreement with the experimental measurements. (author)

Comment on 'Late-time tails of a self-gravitating massless scalar field revisited'

International Nuclear Information System (INIS)

Szpak, Nikodem

2009-01-01

Bizon et al (2009 Class. Quantum Grav. 26 175006) discuss the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in odd spatial dimensions. They derive explicit expressions for the leading-order asymptotics for solutions with small initial data by using formal series expansions. Unfortunately, this approach misses an interesting observation that the actual decay rate is a product of asymptotic cancellations occurring due to a special structure of the nonlinear terms. Here, we show that one can calculate the leading asymptotics more directly by recognizing the special structure and cancellations already on the level of the wave equation. (comments and replies)

Bound states in the (2+1)D scalar electrodynamics with Chern-Simons term

International Nuclear Information System (INIS)

Gomes, M.O.C.; Malacarne, L.C.

1994-01-01

This work studies the existence of bound states for the 3-dimensions scalar electrodynamics, with the Chern-Simons. Quantum field theory is used for calculation of the M fi scattering matrices, in the non-relativistic approximation. The field propagators responsible for the interaction in the scattering processes have been calculated, and scattering matrices have been constructed. After obtaining the scattering matrix, the cross section in the quantum field theory has been compared with the quantum mechanic cross section in the Born approximation, allowing to obtain the form of the potential responsible for the interactions in the scattering processes. The possibility of bound states are analyzed by using the Schroedinger equation

The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

CERN Document Server

Lin, C -J David; Ramos, Alberto

2015-01-01

We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, altho...

Viète's Formula and an Error Bound without Taylor's Theorem

Science.gov (United States)

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

International Nuclear Information System (INIS)

Baikov, P.A.; Chetyrkin, K.G.; Kühn, J.H.

2017-01-01

We extend the O(α s 5 ) result of the analytic calculation of the quark mass anomalous dimension in pQCD https://www.doi.org/10.1007/JHEP10(2014)076 to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

Quasinormal modes of a massless charged scalar field on a small Reissner-Nordstroem-anti-de Sitter black hole

International Nuclear Information System (INIS)

Uchikata, Nami; Yoshida, Shijun

2011-01-01

We investigate quasinormal modes of a massless charged scalar field on a small Reissner-Nordstroem-anti-de Sitter (RN-AdS) black hole both with analytical and numerical approaches. In the analytical approach, by using the small black hole approximation (r + + /L→0, where r + and L stand for the black hole event horizon radius and the AdS scale, respectively. We then show that the small RN-AdS black hole is unstable if its quasinormal modes satisfy the superradiance condition and that the instability condition of the RN-AdS black hole in the limit of r + /L→0 is given by Q>(3/eL)Q c , where Q, Q c , and e are the charge of the black hole, the critical (maximum) charge of the black hole, and the charge of the scalar field, respectively. In the numerical approach, we calculate the quasinormal modes for the small RN-AdS black holes with r + + =0.2L, 0.1L, and 0.01L become unstable against scalar perturbations with eL=4 when the charge of the black hole satisfies Q > or approx. 0.8Q c , 0.78Q c , and 0.76Q c , respectively.

Boson bound states in the β-Fermi–Pasta–Ulam model

Indian Academy of Sciences (India)

The bound states of four bosons in the quantum -Fermi–Pasta–Ulam model are investigated and some interesting results are presented using the number conserving approximation combined ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science

On the Construction of Scattering Amplitudes for Spinning Massless Particles

CERN Document Server

Berends, F A

1997-01-01

In this paper the general form of scattering amplitudes for massless particles with equal spins s ($s s \\to s s$) or unequal spins ($s_a s_b \\to s_a s_b$) are derived. The imposed conditions are that the amplitudes should have the lowest possible dimension, have propagators of dimension $m^{-2}$, and obey gauge invariance. It is shown that the number of momenta required for amplitudes involving particles with s > 2 is higher than the number implied by 3-vertices for higher spin particles derived in the literature. Therefore, the dimension of the coupling constants following from the latter 3-vertices has a smaller power of an inverse mass than our results imply. Consequently, the 3-vertices in the literature cannot be the first interaction terms of a gauge-invariant theory. When no spins s > 2 are present in the process the known QCD, QED or (super) gravity amplitudes are obtained from the above general amplitudes.

Free-space optical communications with peak and average constraints: High SNR capacity approximation

KAUST Repository

Chaaban, Anas

2015-09-07

The capacity of the intensity-modulation direct-detection (IM-DD) free-space optical channel with both average and peak intensity constraints is studied. A new capacity lower bound is derived by using a truncated-Gaussian input distribution. Numerical evaluation shows that this capacity lower bound is nearly tight at high signal-to-noise ratio (SNR), while it is shown analytically that the gap to capacity upper bounds is a small constant at high SNR. In particular, the gap to the high-SNR asymptotic capacity of the channel under either a peak or an average constraint is small. This leads to a simple approximation of the high SNR capacity. Additionally, a new capacity upper bound is derived using sphere-packing arguments. This bound is tight at high SNR for a channel with a dominant peak constraint.

THREE-MOMENT BASED APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING SYSTEMS

Directory of Open Access Journals (Sweden)

T. I. Aliev

2014-03-01

Full Text Available The paper deals with the problem of approximation of probability distributions of random variables defined in positive area of real numbers with coefficient of variation different from unity. While using queueing systems as models for computer networks, calculation of characteristics is usually performed at the level of expectation and variance. At the same time, one of the main characteristics of multimedia data transmission quality in computer networks is delay jitter. For jitter calculation the function of packets time delay distribution should be known. It is shown that changing the third moment of distribution of packets delay leads to jitter calculation difference in tens or hundreds of percent, with the same values of the first two moments – expectation value and delay variation coefficient. This means that delay distribution approximation for the calculation of jitter should be performed in accordance with the third moment of delay distribution. For random variables with coefficients of variation greater than unity, iterative approximation algorithm with hyper-exponential two-phase distribution based on three moments of approximated distribution is offered. It is shown that for random variables with coefficients of variation less than unity, the impact of the third moment of distribution becomes negligible, and for approximation of such distributions Erlang distribution with two first moments should be used. This approach gives the possibility to obtain upper bounds for relevant characteristics, particularly, the upper bound of delay jitter.

Approximate spatio-temporal top-k publish/subscribe

KAUST Repository

Chen, Lisi

2018-04-26

Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

Approximate spatio-temporal top-k publish/subscribe

KAUST Repository

Chen, Lisi; Shang, Shuo

2018-01-01

Location-based publish/subscribe plays a significant role in mobile information disseminations. In this light, we propose and study a novel problem of processing location-based top-k subscriptions over spatio-temporal data streams. We define a new type of approximate location-based top-k subscription, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription, that continuously feeds users with relevant spatio-temporal messages by considering textual similarity, spatial proximity, and information freshness. Different from existing location-based top-k subscriptions, Approximate Temporal Spatial-Keyword Top-k (ATSK) Subscription can automatically adjust the triggering condition by taking the triggering score of other subscriptions into account. The group filtering efficacy can be substantially improved by sacrificing the publishing result quality with a bounded guarantee. We conduct extensive experiments on two real datasets to demonstrate the performance of the developed solutions.

Common approximations for density operators may lead to imaginary entropy

International Nuclear Information System (INIS)

Lendi, K.; Amaral Junior, M.R. do

1983-01-01

The meaning and validity of usual second order approximations for density operators are illustrated with the help of a simple exactly soluble two-level model in which all relevant quantities can easily be controlled. This leads to exact upper bound error estimates which help to select more precisely permissible correlation times as frequently introduced if stochastic potentials are present. A final consideration of information entropy reveals clearly the limitations of this kind of approximation procedures. (Author) [pt

Fast Bound Methods for Large Scale Simulation with Application for Engineering Optimization

Science.gov (United States)

Patera, Anthony T.; Peraire, Jaime; Zang, Thomas A. (Technical Monitor)

2002-01-01

In this work, we have focused on fast bound methods for large scale simulation with application for engineering optimization. The emphasis is on the development of techniques that provide both very fast turnaround and a certificate of Fidelity; these attributes ensure that the results are indeed relevant to - and trustworthy within - the engineering context. The bound methodology which underlies this work has many different instantiations: finite element approximation; iterative solution techniques; and reduced-basis (parameter) approximation. In this grant we have, in fact, treated all three, but most of our effort has been concentrated on the first and third. We describe these below briefly - but with a pointer to an Appendix which describes, in some detail, the current "state of the art."

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

Energy Technology Data Exchange (ETDEWEB)

Baikov, P.A. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,1(2), Leninskie gory, Moscow 119991 (Russian Federation); Chetyrkin, K.G.; Kühn, J.H. [Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT),Wolfgang-Gaede-Straße 1, 726128 Karlsruhe (Germany)

2017-04-20

We extend the O(α{sub s}{sup 5}) result of the analytic calculation of the quark mass anomalous dimension in pQCD https://www.doi.org/10.1007/JHEP10(2014)076 to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

Equations of motion of interacting massless fields of all spins as a free differential algebra

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A

1988-08-11

It is argued that the equations of motion of interacting massless fields of all spins s=0, 1, ..., infinity can naturally be formulated in terms of a free differential algebra (FDA) constructed from one-forms and zero-forms that belong both to the adjoint representation of the infinite-dimensional superalgebra of higher spins and auxiliary fields proposed previously. This FDA is found explicitly in the first non-trivial order in the zero-forms. Various properties of the proposed FDA are discussed including the ways for incorporating internal (Yang-Mills) gauge symmetries via associative algebras.

Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly

International Nuclear Information System (INIS)

Yoshioka, Nobuyuki; Matsuura, Hiroyasu; Ogata, Masao

2016-01-01

We propose a new physical interpretation of the Diophantine equation of σ xy for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called 'subcells', which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of σ xy , that are consistent with the Diophantine equation: Landau quantization of (1) massless Dirac fermions or (2) free fermions in Hofstadter's butterfly. (author)

Zero-point energy of massless scalar fields in the presence of soft and semihard boundaries in D dimensions

International Nuclear Information System (INIS)

Caruso, F.; De Paola, R.; Svaiter, N.F.

1998-06-01

The renormalized energy density of a massless scalar field defined in a D-dimensional flat spacetime is computed in the presence of 'soft'and 'semihard'boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on D for the cases of 'hard'and 'soft/semihard'boundaries area compared. (author)

Bound-Electron Nonlinearity Beyond the Ionization Threshold

Science.gov (United States)

Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

2018-05-01

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Improved Approximation Algorithms for Item Pricing with Bounded Degree and Valuation

Science.gov (United States)

Hamane, Ryoso; Itoh, Toshiya

When a store sells items to customers, the store wishes to decide the prices of the items to maximize its profit. If the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which provides less profit to the store. It would be hard for the store to decide the prices of items. Assume that a store has a set V of n items and there is a set C of m customers who wish to buy those items. The goal of the store is to decide the price of each item to maximize its profit. We refer to this maximization problem as an item pricing problem. We classify the item pricing problems according to how many items the store can sell or how the customers valuate the items. If the store can sell every item i with unlimited (resp. limited) amount, we refer to this as unlimited supply (resp. limited supply). We say that the item pricing problem is single-minded if each customer j∈C wishes to buy a set ej⊆V of items and assigns valuation w(ej)≥0. For the single-minded item pricing problems (in unlimited supply), Balcan and Blum regarded them as weighted k-hypergraphs and gave several approximation algorithms. In this paper, we focus on the (pseudo) degree of k-hypergraphs and the valuation ratio, i. e., the ratio between the smallest and the largest valuations. Then for the single-minded item pricing problems (in unlimited supply), we show improved approximation algorithms (for k-hypergraphs, general graphs, bipartite graphs, etc.) with respect to the maximum (pseudo) degree and the valuation ratio.

Analytic continuation of scattering data to the region of negative energies for systems that have one and two bound states

International Nuclear Information System (INIS)

Blokhintsev, L. D.; Savin, D. A.

2016-01-01

An exactly solvable potential model is used to study the possibility of deducing information about the features of bound states for the system under consideration (binding energies and asymptotic normalization coefficients) on the basis of data on continuum states. The present analysis is based on an analytic approximation and on the subsequent continuation of a partial-wave scattering function from the region of positive energies to the region of negative energies. Cases where the system has one or two bound states are studied. The α+d and α+"1"2C systems are taken as physical examples. In the case of one bound state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation for different polynomial approximations leads to close results, which are nearly coincident with exact values. In the case of two bound states, the scattering function has two poles—one in the region of positive energies and the other in the region of negative energies between the energies corresponding to the two bound states in question. Padéapproximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states.

Approximation of bivariate copulas by patched bivariate Fréchet copulas

KAUST Repository

Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.

2011-01-01

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

Approximation of bivariate copulas by patched bivariate Fréchet copulas

KAUST Repository

Zheng, Yanting

2011-03-01

Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.

Approximate radiative solutions of the Einstein equations

International Nuclear Information System (INIS)

Kuusk, P.; Unt, V.

1976-01-01

In this paper the external field of a bounded source emitting gravitational radiation is considered. A successive approximation method is used to integrate the Einstein equations in Bondi's coordinates (Bondi et al, Proc. R. Soc.; A269:21 (1962)). A method of separation of angular variables is worked out and the approximate Einstein equations are reduced to key equations. The losses of mass, momentum, and angular momentum due to gravitational multipole radiation are found. It is demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In an appendix Bondi's new function is given in terms of sources. (author)

Direct and semi-direct approaches to lepton mixing with a massless neutrino

International Nuclear Information System (INIS)

King, Stephen F.; Ludl, Patrick Otto

2016-01-01

We discuss the possibility of enforcing a massless Majorana neutrino in the direct and semi-direct approaches to lepton mixing, in which the PMNS matrix is partly predicted by subgroups of a discrete family symmetry, extending previous group searches up to order 1535. We find a phenomenologically viable scheme for the semi-direct approach based on Q(648) which contains Δ(27) and the quaternion group as subgroups. This leads to novel predictions for the first column of the PMNS matrix corresponding to a normal neutrino mass hierarchy with m_1=0, and sum rules for the mixing angles and phase which are characterised by the solar angle being on the low side θ_1_2∼31"∘ and the Dirac (oscillation) CP phase δ being either about ±45"∘ or ±π.

No parity anomaly in massless QED{sub 3}: A BPHZL approach

Energy Technology Data Exchange (ETDEWEB)

Del Cima, O.M. [Universidade Federal Fluminense (UFF), Polo Universitario de Rio das Ostras (PURO), Departamento de Ciencia e Tecnologia, Rua Recife s/n, 28890-000, Rio das Ostras, RJ (Brazil)], E-mail: wadodelcima@if.uff.br; Franco, D.H.T. [Universidade Federal de Vicosa (UFV), Departamento de Fisica - Campus Universitario, Avenida Peter Henry Rolfs s/n, 36570-000, Vicosa, MG (Brazil)], E-mail: dhtfranco@gmail.com; Piguet, O. [Universidade Federal do Espirito Santo (UFES), CCE, Departamento de Fisica, Campus Universitario de Goiabeiras, 29060-900, Vitoria, ES (Brazil)], E-mail: opiguet@pq.cnpq.br; Schweda, M. [Institut fuer Theoretische Physik, Technische Universitaet Wien (TU-Wien), Wiedner Hauptstrasse 8-10, A-1040, Vienna (Austria)], E-mail: mschweda@tph.tuwien.ac.at

2009-09-14

In this Letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED{sub 3} frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein-Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern-Simons term is generated at that order induced through the infrared subtractions - which violate parity. We show then that, what is called 'parity anomaly', is in fact a parity-odd counterterm needed for restauring parity.

Application of the negative-dimension approach to massless scalar box integrals

International Nuclear Information System (INIS)

Anastasiou, C.; Glover, E.W.N.; Oleari, C.

2000-01-01

We study massless one-loop box integrals by treating the number of space-time dimensions D as a negative integer. We consider integrals with up to three kinematic scales (s, t and either zero or one off-shell legs) and with arbitrary powers of propagators. For box integrals with q kinematic scales (where q=2 or 3) we immediately obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with q-1 variables, valid for general D. Because the power each propagator is raised to is treated as a parameter, these general expressions are useful in evaluating certain types of two-loop box integrals which are one-loop insertions to one-loop box graphs. We present general expressions for this particular class of two-loop graphs with one off-shell leg, and give explicit representations in terms of polylogarithms in the on-shell case

Improved algorithms for approximate string matching (extended abstract

Directory of Open Access Journals (Sweden)

Papamichail Georgios

2009-01-01

Full Text Available Abstract Background The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. Results We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s - |n - m|·min(m, n, s + m + n and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm also excels in practice, especially in cases where the two strings compared differ significantly in length. Conclusion We have provided the design, analysis and implementation of a new algorithm for calculating the edit distance of two strings with both theoretical and practical implications. Source code of our algorithm is available online.

Circuit lower bounds in bounded arithmetics

Czech Academy of Sciences Publication Activity Database

Pich, Ján

2015-01-01

Roč. 166, č. 1 (2015), s. 29-45 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Keywords : bounded arithmetic * circuit lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.582, year: 2015 http://www.sciencedirect.com/science/article/pii/S0168007214000888

Approximating the Value of a Concurrent Reachability Game in the Polynomial Time Hierarchy

DEFF Research Database (Denmark)

Frederiksen, Søren Kristoffer Stiil; Miltersen, Peter Bro

2013-01-01

We show that the value of a finite-state concurrent reachability game can be approximated to arbitrary precision in TFNP[NP], that is, in the polynomial time hierarchy. Previously, no better bound than PSPACE was known for this problem. The proof is based on formulating a variant of the state red...... reduction algorithm for Markov chains using arbitrary precision floating point arithmetic and giving a rigorous error analysis of the algorithm.......We show that the value of a finite-state concurrent reachability game can be approximated to arbitrary precision in TFNP[NP], that is, in the polynomial time hierarchy. Previously, no better bound than PSPACE was known for this problem. The proof is based on formulating a variant of the state...

Statistical description of massless excitations within a sphere with a linear equation of state and the dark energy case

Science.gov (United States)

Viaggiu, S.

2018-04-01

In this paper, we continue the investigations present in Refs. 1-3. In particular, we extend the theorem proved in Ref. 3 to any massless excitation in a given spherical box. As a first interesting result, we show that it is possible, contrary to the black hole case studied in detail in Refs. 1-3, to build macroscopic configurations with a dark energy equation of state. To this purpose, by requiring a stable configuration, a macroscopic dark fluid is obtained with an internal energy U scaling as the volume V, but with a fundamental correction looking like ˜ 1/R motivated by quantum fluctuations. Thanks to the proposition in Sec. 3 (and in Ref. 3 for gravitons), one can depict the dark energy in terms of massless excitations with a discrete spectrum. This fact opens the possibility to test a possible physical mechanism converting usual radiation into dark energy in a macroscopic configuration, also in a cosmological context. In fact, for example, in a Friedmann flat universe with a cosmological constant, particles are marginally trapped at the Hubble horizon for any given comoving observer.

Scaling Limits and Generic Bounds for Exploration Processes

Science.gov (United States)

Bermolen, Paola; Jonckheere, Matthieu; Sanders, Jaron

2017-12-01

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.

Bound Chains of Tilted Dipoles in Layered Systems

DEFF Research Database (Denmark)

G. Volosniev, A.; R. Armstrong, J.; V. Fedorov, D.

2012-01-01

of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic...... oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account....

Theory of Coulomb drag for massless Dirac fermions

International Nuclear Information System (INIS)

Carrega, M; Principi, A; Polini, M; Tudorovskiy, T; Katsnelson, M I

2012-01-01

Coulomb drag between two unhybridized graphene sheets separated by a dielectric spacer has recently attracted considerable theoretical interest. We first review, for the sake of completeness, the main analytical results which have been obtained by other authors. We then illustrate pedagogically the minimal theory of Coulomb drag between two spatially separated two-dimensional systems of massless Dirac fermions which are both away from the charge-neutrality point. This relies on second-order perturbation theory in the screened interlayer interaction and on Boltzmann-transport theory. In this theoretical framework and in the low-temperature limit, we demonstrate that, to leading (i.e. quadratic) order in temperature, the drag transresistivity is completely insensitive to the precise intralayer momentum-relaxation mechanism (i.e. to the functional dependence of the transport scattering time on energy). We also provide analytical results for the low-temperature drag transresistivity for both cases of ‘thick’ and ‘thin’ spacers and for arbitrary values of the dielectric constants of the media surrounding the two Dirac-fermion layers. Finally, we present numerical results for the low-temperature drag transresistivity for the case when one of the media surrounding the Dirac-fermion layers has a frequency-dependent dielectric constant. We conclude by suggesting an experiment that can potentially allow for the observation of departures from the canonical quadratic-in-temperature behavior of the transresistivity. (paper)

Graphene as an active virtually massless top electrode for RF solidly mounted bulk acoustic wave (SMR-BAW) resonators

Science.gov (United States)

Knapp, Marius; Hoffmann, René; Lebedev, Vadim; Cimalla, Volker; Ambacher, Oliver

2018-03-01

Mechanical and electrical losses induced by an electrode material greatly influence the performance of bulk acoustic wave (BAW) resonators. Graphene as a conducting and virtually massless 2D material is a suitable candidate as an alternative electrode material for BAW resonators which reduces electrode induced mechanical losses. In this publication we show that graphene acts as an active top electrode for solidly mounted BAW resonators (BAW-SMR) at 2.1 GHz resonance frequency. Due to a strong decrease of mass loading and its remarkable electronic properties, graphene demonstrates its ability as an ultrathin conductive layer. In our experiments we used an optimized graphene wet transfer on aluminum nitride-based solidly mounted resonator devices. We achieved more than a triplication of the resonator’s quality factor Q and a resonance frequency close to an ‘unloaded’ resonator without metallization. Our results reveal the direct influence of both, the graphene quality and the graphene contacting via metal structures, on the performance characteristic of a BAW resonator. These findings clearly show the potential of graphene in minimizing mechanical losses due to its virtually massless character. Moreover, they highlight the advantages of graphene and other 2D conductive materials for alternative electrodes in electroacoustic resonators for radio frequency applications.

Massless charged particles: Cosmic censorship, and the third law of black hole mechanics

Science.gov (United States)

Fairoos, C.; Ghosh, Avirup; Sarkar, Sudipta

2017-10-01

The formulation of the laws of Black hole mechanics assumes the stability of black holes under perturbations in accordance with the "cosmic censorship hypothesis" (CCH). CCH prohibits the formation of a naked singularity by a physical process from a regular black hole solution with an event horizon. Earlier studies show that naked singularities can indeed be formed leading to the violation of CCH if a near-extremal black hole is injected with massive charged particles and the backreaction effects are neglected. We investigate the validity of CCH by considering the infall of charged massless particles as well as a charged null shell. We also discuss the issue of the third law of Black hole mechanics in the presence of null charged particles by considering various possibilities.

Simple Lie groups without the approximation property

DEFF Research Database (Denmark)

Haagerup, Uffe; de Laat, Tim

2013-01-01

For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...

Low-temperature excitations within the Bethe approximation

International Nuclear Information System (INIS)

Biazzo, I; Ramezanpour, A

2013-01-01

We propose the variational quantum cavity method to construct a minimal energy subspace of wavevectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wavefunction we use the cavity method of statistical physics to estimate the Hamiltonian expectation and to find the optimal variational parameters in the subspace of wavevectors orthogonal to the lower-energy wavefunctions. To this end, we write the overlap between two wavefunctions within the Bethe approximation, which allows us to replace the global orthogonality constraint with some local constraints on the variational parameters. The method is applied to the transverse Ising model and different levels of approximations are compared with the exact numerical solutions for small systems. (paper)

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

Science.gov (United States)

Barth, Timothy J.

2014-01-01

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

On Nash-Equilibria of Approximation-Stable Games

Science.gov (United States)

Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

Numerical evaluation of virtual corrections to multi-jet production in massless QCD

DEFF Research Database (Denmark)

Badger, S.; Yundin, V.; Biedermann, B.

2013-01-01

title: NJet. Catalogue identifier: AEPF_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPF_v1_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU General Public License, version 3. No. of lines in distributed program......, including test data, etc.: 250047. No. of bytes in distributed program, including test data, etc.: 2138947. Distribution format: tar.gz. Programming language: C++, Python. Computer: PC/Workstation. Operating system: No specific requirements - tested on Scientific Linux 5.2. and Mac OS X 10.......7.4. Classification: 11.5. External routines: QCDLoop (http://qcdloop.fnal.gov/), qd (http://crd.lbl.gov/dhbailey/mpdist/), both included in the distribution file. Nature of problem:. Evaluation of virtual corrections for multi-jet production in massless QCD. Solution method:. Purely numerical approach based on tree...

Approximation of ruin probabilities via Erlangized scale mixtures

DEFF Research Database (Denmark)

Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue

2018-01-01

In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....

High energy approximations for nuclear knockout form factors at small momentum transfer

International Nuclear Information System (INIS)

Amado, R.D.; Cannata, F.; Dedonder, J.P.

1985-01-01

We obtain an explicit approximate expression for the nucleon knockout form factor at small momentum transfer induced by a scalar probe in a single particle model in terms of the momentum space bound state wave function. Our form preserves the orthogonality constraint without using explicitly the final state scattering wave function. We examine the leading large momentum behavior of the momentum space wave function and of correction terms to our expression for the form factor in the case where the bound state is an s state

Relativistic treatment of fermion-antifermion bound states

International Nuclear Information System (INIS)

Lucha, W.; Rupprecht, H.; Schoeberl, F.F.

1990-01-01

We discuss the relativistic treatment of fermion-antifermion bound states by an effective-Hamiltonian method which imitates their description in terms of nonrelativistic potential models: the effective interaction potential, to be used in a Schroedinger equation which incorporates relativistic kinematics, is derived from the underlying quantum field theory. This approach is equivalent to the instantaneous approximation to the Bethe-Salpeter equation called Salpeter equation but comes closer to physical intuition than the latter one. (Author) 14 refs

Information theoretic bounds for compressed sensing in SAR imaging

International Nuclear Information System (INIS)

Jingxiong, Zhang; Ke, Yang; Jianzhong, Guo

2014-01-01

Compressed sensing (CS) is a new framework for sampling and reconstructing sparse signals from measurements significantly fewer than those prescribed by Nyquist rate in the Shannon sampling theorem. This new strategy, applied in various application areas including synthetic aperture radar (SAR), relies on two principles: sparsity, which is related to the signals of interest, and incoherence, which refers to the sensing modality. An important question in CS-based SAR system design concerns sampling rate necessary and sufficient for exact or approximate recovery of sparse signals. In the literature, bounds of measurements (or sampling rate) in CS have been proposed from the perspective of information theory. However, these information-theoretic bounds need to be reviewed and, if necessary, validated for CS-based SAR imaging, as there are various assumptions made in the derivations of lower and upper bounds on sub-Nyquist sampling rates, which may not hold true in CS-based SAR imaging. In this paper, information-theoretic bounds of sampling rate will be analyzed. For this, the SAR measurement system is modeled as an information channel, with channel capacity and rate-distortion characteristics evaluated to enable the determination of sampling rates required for recovery of sparse scenes. Experiments based on simulated data will be undertaken to test the theoretic bounds against empirical results about sampling rates required to achieve certain detection error probabilities

Spacecraft attitude control using neuro-fuzzy approximation of the optimal controllers

Science.gov (United States)

Kim, Sung-Woo; Park, Sang-Young; Park, Chandeok

2016-01-01

In this study, a neuro-fuzzy controller (NFC) was developed for spacecraft attitude control to mitigate large computational load of the state-dependent Riccati equation (SDRE) controller. The NFC was developed by training a neuro-fuzzy network to approximate the SDRE controller. The stability of the NFC was numerically verified using a Lyapunov-based method, and the performance of the controller was analyzed in terms of approximation ability, steady-state error, cost, and execution time. The simulations and test results indicate that the developed NFC efficiently approximates the SDRE controller, with asymptotic stability in a bounded region of angular velocity encompassing the operational range of rapid-attitude maneuvers. In addition, it was shown that an approximated optimal feedback controller can be designed successfully through neuro-fuzzy approximation of the optimal open-loop controller.

Approximately dual frames in Hilbert spaces and applications to Gabor frames

DEFF Research Database (Denmark)

Christensen, Ole; Laugesen, Richard S.

2011-01-01

constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in the duality conditions. To illustrate these results, we construct explicit approximate duals of Gabor...

Perceptron Mistake Bounds

OpenAIRE

Mohri, Mehryar; Rostamizadeh, Afshin

2013-01-01

We present a brief survey of existing mistake bounds and introduce novel bounds for the Perceptron or the kernel Perceptron algorithm. Our novel bounds generalize beyond standard margin-loss type bounds, allow for any convex and Lipschitz loss function, and admit a very simple proof.

Two-dimensional massless quantum electrodynamics in the Landau-gauge formalism and the Higgs mechanism

International Nuclear Information System (INIS)

Ito, K.R.

1975-01-01

The Schwinger model is considered in the Landau-gauge formalism of quantum electrodynamics. This model can be solved exactly on the assumption of no radiative corrections to the anomaly. It is found that the photon obtains a non-zero mass through the Higgs mechanism. In this case, the would-be Nambu-Goldstone boson is an associated boson which is constructed from a pair of two-component massless fermions. This would-be Nambu-Goldstone boson appears as a result of the spontaneous breaking of the gauge invariance of the first kind, and it becomes unphysical through the Higgs mechanism. However, as all the fermions themselves decouple from photons, they cannot appear as real particles in our world. (author)

Two approximations of the present value distribution of a disability annuity

Science.gov (United States)

Spreeuw, Jaap

2006-02-01

The distribution function of the present value of a cash flow can be approximated by means of a distribution function of a random variable, which is also the present value of a sequence of payments, but with a simpler structure. The corresponding random variable has the same expectation as the random variable corresponding to the original distribution function and is a stochastic upper bound of convex order. A sharper upper bound can be obtained if more information about the risk is available. In this paper, it will be shown that such an approach can be adopted for disability annuities (also known as income protection policies) in a three state model under Markov assumptions. Benefits are payable during any spell of disability whilst premiums are only due whenever the insured is healthy. The quality of the two approximations is investigated by comparing the distributions obtained with the one derived from the algorithm presented in the paper by Hesselager and Norberg [Insurance Math. Econom. 18 (1996) 35-42].

Bethe-Salpeter equation for fermion-antifermion system in the ladder approximation

International Nuclear Information System (INIS)

Fukui, Ichio; Seto, Noriaki; Yoshida, Toshihiro.

1977-01-01

The Bethe-Salpeter (B-S) equation is important for studying hadron physics. Especially intensive investigation on the fermion-antifermion B-S equation is indispensable for the phenomenological studies of hardrons. However, many components of the B-S amplitude and the Wick-rotated integral kernel of non-Fredholm type have prevented from knowing details the solutions even in the ladder approximation. Some particular solutions are known in case of the vanishing four-momenta of bound states. The B-S equation for the bound state of fermion-anti-fermion system interacting through vector (axial-vector) particle exchange was studied in the ladder approximation with Feynman gauge. The reduced equations were obtained for suitably decomposed amplitude, and it is shown that, in the S-wave case, the coupled equations separate into two parts. In the nonrelativistic limit, large components of the amplitude satisfy the Wick-Cutkosky equation, and small components are expressed in terms of the large ones. Equations are derived for the equal-time amplitudes. (Kobatake, H.)

Approximate Networking for Universal Internet Access

Directory of Open Access Journals (Sweden)

Junaid Qadir

2017-12-01

Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.

Proton induced nucleon knockout from 40Ca in the Dirac impulse approximation

International Nuclear Information System (INIS)

Maxwell, O.V.; Cooper, E.D.

1989-12-01

The (p,2p) reaction on 40 Ca at incident proton energies of 200 and 300 MeV is examined within a Dirac distorted wave impulse approximation. The relativistic Love-Franey t-matrix is evaluated at the nucleon-nucleon laboratory energy (as defined within the plane wave approximation), rather than the nucleon-nucleus laboratory energy. Particular attention is paid to the sensitivity of the calculated cross sections and analyzing powers to the properties of the bound states employed. It is found that the analyzing powers depend very little on the bound state properties, while the cross sections depend significantly only on the rms radii of the bound state wave functions. A major success of the model is its ability to fit the cross section data over a particular range of momentum transfers at both 200 and 300 MeV with the same bound state potential. Outside this momentum transfer range, the predicted cross sections are too low. The calculated analyzing powers agree well with the data at 200 MeV, but disagree with the data at 300 MeV. Values for the rms radii of the 1D 3/2 and 1D 5/2 states in 40 Ca are derived from the requirement that the peak positions of the calculated cross sections at 300 MeV agree with the empirical peak positions. Some preliminary results are also reported for neutron knockout from 40 Ca at 150 MeV

Three-Way Channels With Multiple Unicast Sessions: Capacity Approximation via Network Transformation

KAUST Repository

Chaaban, Anas

2016-09-28

A network of three nodes mutually communicating with each other is studied. This multi-way network is a suitable model for three-user device-to-device communications. The main goal of this paper is to characterize the capacity region of the underlying Gaussian three-way channel (3WC) within a constant gap. To this end, a capacity outer bound is derived using cut-set bounds and genie-aided bounds. For achievability, the 3WC is first transformed into an equivalent star channel. This latter is then decomposed into a set of “successive” sub-channels, leading to a sub-channel allocation problem. Using backward decoding, interference neutralization, and known results on the capacity of the star-channel relying of physical-layer network coding, an achievable rate region for the 3WC is obtained. It is then shown that the achievable rate region is within a constant gap of the developed outer bound, leading to the desired capacity approximation. Interestingly, in contrast to the Gaussian two-way channel (TWC), adaptation is necessary in the 3WC. Furthermore, message splitting is another ingredient of the developed scheme for the 3WC, which is not required in the TWC. The two setups are, however, similar in terms of their sum-capacity pre-log, which is equal to 2. Finally, some interesting networks and their approximate capacities are recovered as special cases of the 3WC, such as the cooperative broadcast channel and multiple access channel.

Spinless Salpeter equation: Laguerre bounds on energy levels

International Nuclear Information System (INIS)

Lucha, W.; Schoeberl, F.F.

1996-08-01

The spinless Salpeter equation may be considered either as a standard approximation to the Bethe-Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the customary non relativistic Schroedinger formalism. Because of the presence of the rather difficult-to-handle square-root operator of the relativistic kinetic energy in the corresponding Hamiltonian, very frequently the corresponding (discrete) spectrum of energy eigenvalues cannot be determined analytically. Therefore, we show how to calculate, by some clever choice of basis vectors in the Hilbert space of solutions, for the rather large class of power-law potentials, at least (sometimes excellent) upper bounds on these energy eigenvalues, for the lowest-lying levels this even analytically. (author)

Iterative approximation of the solution of a monotone operator equation in certain Banach spaces

International Nuclear Information System (INIS)

Chidume, C.E.

1988-01-01

Let X=L p (or l p ), p ≥ 2. The solution of the equation Ax=f, f is an element of X is approximated in X by an iteration process in each of the following two cases: (i) A is a bounded linear mapping of X into itself which is also bounded below; and, (ii) A is a nonlinear Lipschitz mapping of X into itself and satisfies ≥ m |x-y| 2 , for some constant m > 0 and for all x, y in X, where j is the single-valued normalized duality mapping of X into X* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X. (author). 12 refs

Spin symmetry in the relativistic symmetrical well potential including a proper approximation to the spin-orbit coupling term

International Nuclear Information System (INIS)

Wei Gaofeng; Dong Shihai

2010-01-01

In the case of exact spin symmetry, we approximately solve the Dirac equation with scalar and vector symmetrical well potentials by using a proper approximation to the spin-orbit coupling term, and obtain the corresponding energy equation and spinor wave functions for the bound states. We find that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter α goes to zero. The special case for equally scalar and vector symmetrical well potentials is studied briefly.

All the fundamental massless bosonic fields in superstring theory

International Nuclear Information System (INIS)

Manoukian, E.B.

2012-01-01

A systematic analysis of all the massless bosonic fields in superstring theory is carried out. Emphasis is put on the derivation of their propagators, their polarization aspects and the investigation of their underlying constraints as well as their number of degrees of freedom. The treatment is given in the presence of external sources, in the celebrated Coulomb gauge, ensuring the positivity of the formalism - a result which is also established in the process. The challenge here is the investigation involved in the self-dual fourth rank anti-symmetric tensor field. No constraints are imposed on the external sources so that their components may be varied independently, thus the complete expressions of the propagators may be obtained. As emphasized in our earlier work, the latter condition is an important one in dynamical theories with constraints giving rise to modifications as Faddeev-Popov factors. The analysis is carried out in 10 dimensions, not only because of the consistency requirement by the superstrings, but also in order to take into account of the self-duality character of the fourth rank anti-symmetric tensor field as spelled out in the paper. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

International Nuclear Information System (INIS)

Wei Gaofeng; Dong Shihai

2008-01-01

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential

Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

International Nuclear Information System (INIS)

Chen Changyuan; Sun Dongsheng; Lu Falin

2007-01-01

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

Dynamics of entropic uncertainty for atoms immersed in thermal fluctuating massless scalar field

Science.gov (United States)

Huang, Zhiming

2018-04-01

In this article, the dynamics of quantum memory-assisted entropic uncertainty relation for two atoms immersed in a thermal bath of fluctuating massless scalar field is investigated. The master equation that governs the system evolution process is derived. It is found that the mixedness is closely associated with entropic uncertainty. For equilibrium state, the tightness of uncertainty vanishes. For the initial maximum entangled state, the tightness of uncertainty undergoes a slight increase and then declines to zero with evolution time. It is found that temperature can increase the uncertainty, but two-atom separation does not always increase the uncertainty. The uncertainty evolves to different relatively stable values for different temperatures and converges to a fixed value for different two-atom distances with evolution time. Furthermore, weak measurement reversal is employed to control the entropic uncertainty.

Energy quantization for approximate H-surfaces and applications

Directory of Open Access Journals (Sweden)

Shenzhou Zheng

2013-07-01

Full Text Available We consider weakly convergent sequences of approximate H-surface maps defined in the plane with their tension fields bounded in $L^p$ for p> 4/3, and establish an energy quantization that accounts for the loss of their energies by the sum of energies over finitely many nontrivial bubbles maps on $mathbb{R}^2$. As a direct consequence, we establish the energy identity at finite singular time to their H-surface flows.

Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

KAUST Repository

Nielsen, Frank

2016-12-09

Information-theoreticmeasures, such as the entropy, the cross-entropy and the Kullback-Leibler divergence between two mixture models, are core primitives in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy, the Kullback-Leibler and the α-divergences of mixtures. We illustrate the versatile method by reporting our experiments for approximating the Kullback-Leibler and the α-divergences between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures and Gamma mixtures.

Anomalous Diffusion Approximation of Risk Processes in Operational Risk of Non-Financial Corporations

Science.gov (United States)

Magdziarz, M.; Mista, P.; Weron, A.

2007-05-01

We introduce an approximation of the risk processes by anomalous diffusion. In the paper we consider the case, where the waiting times between successive occurrences of the claims belong to the domain of attraction of alpha -stable distribution. The relationship between the obtained approximation and the celebrated fractional diffusion equation is emphasised. We also establish upper bounds for the ruin probability in the considered model and give some numerical examples.

Gravitational recoil from binary black hole mergers: The close-limit approximation

International Nuclear Information System (INIS)

Sopuerta, Carlos F.; Yunes, Nicolas; Laguna, Pablo

2006-01-01

The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. Due to the relevance of this phenomenon in astrophysics, in particular, for galaxy merger scenarios, there have been several attempts to estimate the magnitude of this velocity. Since the main contribution to the recoil comes from the last orbit and plunge, an approximation valid at the last stage of coalescence is well motivated for this type of calculation. In this paper, we present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of ∼57 km/s for a symmetric mass ratio η=M 1 M 2 /(M 1 +M 2 ) 2 ∼0.19 and an initial proper separation of 4M, where M is the total Arnowitt-Deser-Misner (ADM) mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. Therefore, it cannot account for the contributions due to inspiral and initial merger. If we supplement this estimate with post-Newtonian (PN) calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around 80 km/s. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of 214-240 km/s. We also provide nonlinear fits to these estimated upper and lower bounds. These

Convex order approximations in case of cash flows of mixed signs

NARCIS (Netherlands)

Dhaene, J.; Goovaerts, M.J.; Vanmaele, M.; van Weert, K.

2012-01-01

In Van Weert et al. (2010), results are obtained showing that, when allowing some of the cash flows to be negative, convex order lower bound approximations can still be used to solve general investment problems in a context of provisioning or terminal wealth. In this paper, a correction and further

More on equations of motion for interacting massless field of all spins in 3+1 dimensions

Energy Technology Data Exchange (ETDEWEB)

Vasiliev, M A [Inst. of Theoretical Physics, Goteborg (Sweden)

1992-07-09

We establish the simple link between the recently proposed equations of motion for interacting massless fields of all spins 0{<=}s<{infinity} in 3+1 dimensions and conventional formulations of free higher-spin dynamics. In addition, we discuss various types of formal generalizations of the system of equations of Vasiliev which may give rise to interesting relativistic systems in 2+1 and 3+1 dimensions. In particular, it is shown that there exists a class of equations generalizing Vasiliev's system, parametrized by an arbitrary function of one variable. Self-dual higher-spin equations are discussed briefly. (orig.).

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Science.gov (United States)

Göschl, Daniel

2018-03-01

We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

Investigations into light-front interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes

Energy Technology Data Exchange (ETDEWEB)

Bengtsson, Anders K.H. [Academy of Textiles, Engineering and Economics, University of Borås,Allégatan 1, SE-50190 Borås (Sweden)

2016-12-27

The dynamical commutators of the light-front Poincaré algebra yield first order differential equations in the p{sup +} momenta for the interaction vertex operators. The homogeneous solution to the equation for the quartic vertex is studied. Consequences as regards the constructibility assumption of quartic higher spin amplitudes from cubic amplitudes are discussed. The existence of quartic contact interactions unrelated to cubic interactions by Poincaré symmetry indicates that the higher spin S-matrix is not constructible. Thus quartic amplitude based no-go results derived by BCFW recursion for Minkowski higher spin massless fields may be circumvented.

On the mathematical treatment of the Born-Oppenheimer approximation

International Nuclear Information System (INIS)

Jecko, Thierry

2014-01-01

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

On the mathematical treatment of the Born-Oppenheimer approximation

Energy Technology Data Exchange (ETDEWEB)

Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

2014-05-15

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

Electromagnetic structure of a bound nucleon

International Nuclear Information System (INIS)

Nogami, Y.

1977-01-01

The effect of binding on the electromagnetic (e.m.) structure of a nucleon in a nucleus is examined by means of a model consisting of a single nucleon which is bound in a harmonic oscillator potential and also coupled to the pion field through the Chew-Low interaction. The 'two-pion contribution' to the e.m. structure is considered. This is the part which is probably most susceptible to the binding effect. By the binding effect it is meant the one which arises because the nucleon wave functions, in the intermediate state as well as in the initial and final states, are distorted by the potential in which the nucleon is bound. This may be compared to a similar correction to the impulse approximation for pion-nucleus scattering. Unlike the latter which is likely to be quite appreciable, the binding correction to the e.m. structure of the nucleon is found to be negligibly small. The so-called quenching effect due to the Pauli principle when there are other nucleons is also discussed [pt

Bounded Perturbation Regularization for Linear Least Squares Estimation

KAUST Repository

Ballal, Tarig

2017-10-18

This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

Monitoring orientation and dynamics of membrane-bound melittin utilizing dansyl fluorescence.

Science.gov (United States)

Haldar, Sourav; Raghuraman, H; Chattopadhyay, Amitabha

2008-11-06

Melittin is a cationic hemolytic peptide isolated from the European honey bee, Apis mellifera. In spite of a number of studies, there is no consensus regarding the orientation of melittin in membranes. In this study, we used a melittin analogue that is covalently labeled at its amino terminal (Gly-1) with the environment-sensitive 1-dimethylamino-5-sulfonylnaphthalene (dansyl) group to obtain information regarding the orientation and dynamics of the amino terminal region of membrane-bound melittin. Our results show that the dansyl group in Dns-melittin exhibits red edge excitation shift in vesicles of 1,2-dioleoyl-sn-glycero-3-phosphocholine, implying its localization in a motionally restricted region of the membrane. This is further supported by wavelength-dependent anisotropy and lifetime changes and time-resolved emission spectra characterized by dynamic Stokes shift, which indicates relatively slow solvent relaxation in the excited state. Membrane penetration depth analysis using the parallax method shows that the dansyl group is localized at a depth of approximately 18 A from the center of the bilayer in membrane-bound Dns-melittin. Further analysis of dansyl and tryptophan depths in Dns-melittin shows that the tilt angle between the helix axis of membrane-bound melittin and the bilayer normal is approximately 70 degrees. Our results therefore suggest that melittin adopts a pseudoparallel orientation in DOPC membranes at low concentration.

Applications of Some Classes of Sequences on Approximation of Functions (Signals by Almost Generalized Nörlund Means of Their Fourier Series

Directory of Open Access Journals (Sweden)

Xhevat Z. Krasniqi

2015-11-01

Full Text Available In this paper, using rest bounded variation sequences and head bounded variation sequences, some new results on approximation of functions (signals by almost generalized Nörlund means of their Fourier series are obtained. To our best knowledge this the first time to use such classes of sequences on approximations of the type treated in this paper. In addition, several corollaries are derived from our results as well as those obtained previously by others.

On the Distribution of Zeros and Poles of Rational Approximants on Intervals

Directory of Open Access Journals (Sweden)

V. V. Andrievskii

2012-01-01

Full Text Available The distribution of zeros and poles of best rational approximants is well understood for the functions (=||, >0. If ∈[−1,1] is not holomorphic on [−1,1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [−1,1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, -values, and poles of best real rational approximants of degree at most to a function ∈[−1,1] that is real-valued, but not holomorphic on [−1,1]. Generalizations to the lower half of the Walsh table are indicated.

Action-angle variables for the massless relativistic string in 1+1 dimensions

International Nuclear Information System (INIS)

Soederberg, B.; Andersson, B.; Gustafson, G.

1985-01-01

In this paper the Poisson bracket algebra for the open massless relativistic string in the one-space- and one-time-dimensional case is considered. In order to characterize the orbit of the system the directrix function, i.e., the orbit of one of the endpoints of the string, is used. It turns out that the Poisson bracket algebra is of a very simple form in terms of the parameters of the directrix function. We use these results to construct action-angle variables for the general motion of the string. The variables are different for different Lorentz frames, with a continuous dependence. The action-angle variables of the center-of-mass frame and of the light-cone frames are of particular interest with respect to the simplicity of the Poincare generators and the physical interpretation. For the light-cone frame variables the equivalence to a set of indistinguishable oscillators is shown, for which an excitation corresponds to an instantaneous momentum transfer to an endpoint of the string

Cross section evaluation by spinor integration: The massless case in 4D

International Nuclear Information System (INIS)

Feng Bo; Huang Rijun; Jia Yin; Luo Mingxing; Wang Honghui

2010-01-01

To get the total cross section of one interaction from its amplitude M, one needs to integrate |M| 2 over phase spaces of all outgoing particles. Starting from this paper, we will propose a new method to perform such integrations, which is inspired by the reduced phase space integration of one-loop unitarity cut developed in the last few years. The new method reduces one constrained three-dimension momentum space integration to a one-dimensional integration, plus one possible Feynman parameter integration. There is no need to specify a reference framework in our calculation, since every step is manifestly Lorentz invariant by the new method. The current paper is the first paper of a series for the new method. Here we have exclusively focused on massless particles in 4D. There is no need to carve out a complicated integration region in the phase space for this particular simple case because the integration region is always simply [0,1].

Capacity Bounds and High-SNR Capacity of MIMO Intensity-Modulation Optical Channels

KAUST Repository

Chaaban, Anas

2018-02-19

The capacity of the intensity modulation direct detection multiple-input multiple-output channel is studied. Therein, the nonnegativity constraint of the transmit signal limits the applicability of classical schemes, including precoding. Thus, new ways are required for deriving capacity bounds for this channel. To this end, capacity lower bounds are developed in this paper by deriving the achievable rates of two precodingfree schemes: Channel inversion and QR decomposition. The achievable rate of a DC-offset SVD-based scheme is also derived as a benchmark. Then, capacity upper bounds are derived and compared against the lower bounds. As a result, the capacity at high signal-to-noise ratio (SNR) is characterized for the case where the number of transmit apertures is not larger than the number of receive apertures, and is shown to be achievable by the QR decomposition scheme. This is shown for a channel with average intensity or peak intensity constraints. Under both constraints, the high-SNR capacity is approximated within a small gap. Extensions to a channel with more transmit apertures than receive apertures are discussed, and capacity bounds for this case are derived.

Capacity Bounds and High-SNR Capacity of MIMO Intensity-Modulation Optical Channels

KAUST Repository

Chaaban, Anas; Rezki, Zouheir; Alouini, Mohamed-Slim

2018-01-01

The capacity of the intensity modulation direct detection multiple-input multiple-output channel is studied. Therein, the nonnegativity constraint of the transmit signal limits the applicability of classical schemes, including precoding. Thus, new ways are required for deriving capacity bounds for this channel. To this end, capacity lower bounds are developed in this paper by deriving the achievable rates of two precodingfree schemes: Channel inversion and QR decomposition. The achievable rate of a DC-offset SVD-based scheme is also derived as a benchmark. Then, capacity upper bounds are derived and compared against the lower bounds. As a result, the capacity at high signal-to-noise ratio (SNR) is characterized for the case where the number of transmit apertures is not larger than the number of receive apertures, and is shown to be achievable by the QR decomposition scheme. This is shown for a channel with average intensity or peak intensity constraints. Under both constraints, the high-SNR capacity is approximated within a small gap. Extensions to a channel with more transmit apertures than receive apertures are discussed, and capacity bounds for this case are derived.

Learning with Generalization Capability by Kernel Methods of Bounded Complexity

Czech Academy of Sciences Publication Activity Database

Kůrková, Věra; Sanguineti, M.

2005-01-01

Roč. 21, č. 3 (2005), s. 350-367 ISSN 0885-064X R&D Projects: GA AV ČR 1ET100300419 Institutional research plan: CEZ:AV0Z10300504 Keywords : supervised learning * generalization * model complexity * kernel methods * minimization of regularized empirical errors * upper bounds on rates of approximate optimization Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2005

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

Science.gov (United States)

Wolpert, David H.

2005-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Stochastic integration of the Bethe-Salpeter equation for two bound fermions

International Nuclear Information System (INIS)

Salomon, M.

1988-09-01

A non-perturbative method using a Monte Carlo algorithm is used to integrate the Bethe-Salpeter equation in momentum space. Solutions for two scalars and two fermions with an arbitrary coupling constant are calculated for bound states in the ladder approximation. The results are compared with other numerical methods. (Author) (13 refs., 2 figs.)

Virial Expansion Bounds

Science.gov (United States)

Tate, Stephen James

2013-10-01

In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.

Upper bounds on superpartner masses from upper bounds on the Higgs boson mass.

Science.gov (United States)

Cabrera, M E; Casas, J A; Delgado, A

2012-01-13

The LHC is putting bounds on the Higgs boson mass. In this Letter we use those bounds to constrain the minimal supersymmetric standard model (MSSM) parameter space using the fact that, in supersymmetry, the Higgs mass is a function of the masses of sparticles, and therefore an upper bound on the Higgs mass translates into an upper bound for the masses for superpartners. We show that, although current bounds do not constrain the MSSM parameter space from above, once the Higgs mass bound improves big regions of this parameter space will be excluded, putting upper bounds on supersymmetry (SUSY) masses. On the other hand, for the case of split-SUSY we show that, for moderate or large tanβ, the present bounds on the Higgs mass imply that the common mass for scalars cannot be greater than 10(11)  GeV. We show how these bounds will evolve as LHC continues to improve the limits on the Higgs mass.

Finite element approximation to a model problem of transonic flow

International Nuclear Information System (INIS)

Tangmanee, S.

1986-12-01

A model problem of transonic flow ''the Tricomi equation'' in Ω is contained in IR 2 bounded by the rectangular-curve boundary is posed in the form of symmetric positive differential equations. The finite element method is then applied. When the triangulation of Ω-bar is made of quadrilaterals and the approximation space is the Lagrange polynomial, we get the error estimates. 14 refs, 1 fig

Upper and lower bounds for disadvantage factors as a test of an algorithm used in a synthesis method

International Nuclear Information System (INIS)

Ackroyd, R.T.; Nanneh, M.M.

1988-01-01

A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for urnaium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa. (author)

The DMM Bound

DEFF Research Database (Denmark)

Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias

2010-01-01

) resultant by means of mixed volume, as well as recent advances on aggregate root bounds for univariate polynomials, and are applicable to arbitrary positive dimensional systems. We improve upon Canny's gap theorem [7] by a factor of O(dn-1), where d bounds the degree of the polynomials, and n is the number...... bound on the number of steps that subdivision-based algorithms perform in order to isolate all real roots of a polynomial system. This leads to the first complexity bound of Milne's algorithm [22] in 2D....

Estimating the Probabilities of Low-Weight Differential and Linear Approximations on PRESENT-like Ciphers

DEFF Research Database (Denmark)

Abdelraheem, Mohamed Ahmed

2012-01-01

We use large but sparse correlation and transition-difference-probability submatrices to find the best linear and differential approximations respectively on PRESENT-like ciphers. This outperforms the branch and bound algorithm when the number of low-weight differential and linear characteristics...

Bounds and asymptotics for orthogonal polynomials for varying weights

CERN Document Server

Levin, Eli

2018-01-01

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.  Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics.  This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .

Proton-bound cluster ions in ion mobility spectrometry

Science.gov (United States)

Ewing, R. G.; Eiceman, G. A.; Stone, J. A.

1999-01-01

Gaseous oxygen and nitrogen bases, both singly and as binary mixtures, have been introduced into ion mobility spectrometers to study the appearance of protonated molecules, and proton-bound dimers and trimers. At ambient temperature it was possible to simultaneously observe, following the introduction of molecule A, comparable intensities of peaks ascribable to the reactant ion (H2O)nH+, the protonated molecule AH+ and AH+ H2O, and the symmetrical proton bound dimer A2H+. Mass spectral identification confirmed the identifications and also showed that the majority of the protonated molecules were hydrated and that the proton-bound dimers were hydrated to a much lesser extent. No significant peaks ascribable to proton-bound trimers were obtained no matter how high the sample concentration. Binary mixtures containing molecules A and B, in some cases gave not only the peaks unique to the individual compounds but also peaks due to asymmetrical proton bound dimers AHB+. Such ions were always present in the spectra of mixtures of oxygen bases but were not observed for several mixtures of oxygen and nitrogen bases. The dimers, which were not observable, notable for their low hydrogen bond strengths, must have decomposed in their passage from the ion source to the detector, i.e. in a time less than approximately 5 ms. When the temperature was lowered to -20 degrees C, trimers, both homogeneous and mixed, were observed with mixtures of alcohols. The importance of hydrogen bond energy, and hence operating temperature, in determining the degree of solvation of the ions that will be observed in an ion mobility spectrometer is stressed. The possibility is discussed that a displacement reaction involving ambient water plays a role in the dissociation.

Instability of hot electroweak theory: Bounds on mH and mt

International Nuclear Information System (INIS)

Arnold, P.; Vokos, S.

1991-01-01

The electroweak vacuum need not be absolutely stable. For certain top-quark and Higgs-boson masses in the minimal standard model, it is instead metastable with a lifetime exceeding the present age of the Universe. The decay of our vacuum may be nucleated at low temperature by quantum tunneling or at high temperature by thermal excitation. We show that the requirement that the vacuum survive the high temperatures of the early Universe places the strongest constraints from vacuum stability on the top-quark and Higgs-boson masses in the minimal standard model. If a single Higgs boson is found experimentally, these constraints may place an upper bound on the scale of new physics beyond the minimal standard model. In contrast with other work, we examine temperatures very large compared to the scale of weak symmetry restoration and find much stronger bounds. We also present a simple analytic approximation that directly relates the bounds to the running coupling constants of the minimal standard model

Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions

International Nuclear Information System (INIS)

Eab, C. H.; Lim, S. C.; Teo, L. P.

2007-01-01

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed

Vacuum state structure and the screening mechanism of a charge in two-dimensional massless electrodynamics

International Nuclear Information System (INIS)

Danilov, G.S.; Dyatlov, I.T.; Petrov, V.Yu.

1982-01-01

In two-dimensional electrodynamics (QED 2 ) of massless fermions (quarks) the screening and confinement of a charge is due to the transition of local charges into vacuum of the system under the action of the field changing the topological number. An exact solution of the problem of the quark structure of vacuum for two variants of QED 2 shows that it is consistent with the phenomenon. The structure of vacuum is therefore related directly to the Adler anomaly and to the character of variation of the field topological numbers in dynamic processes. The solutions obtained permit one to investigate in an explicit form the properties of a chiral condensate, the existence of which is also a direct consequence of the Adler anomaly

Approximating Frequent Items in Asynchronous Data Stream over a Sliding Window

DEFF Research Database (Denmark)

Ting, Hing-Fung; Lee, Lap Kei; Chan, Ho-Leung

2011-01-01

with sufficient accuracy. Prior to our work, the best solution is given by Cormode et al. [1], who gave an O (1/ε log W log (εB/ log W) min {log W, 1/ε} log |U|)- space data structure that can approximate the frequent items within an ε error bound, where W and B are parameters of the sliding window, and U...

Upper and lower bounds for disadvantage factors as a test of algorithm used in a synthesis method

International Nuclear Information System (INIS)

Nanneh, M.M.; Ackroyd, R.T.

1991-01-01

A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for uranium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa. (author). 15 refs., 8 tabs., 9 figs

Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

KAUST Repository

Nielsen, Frank; Sun, Ke

2016-01-01

does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. We present a fast and generic method that builds algorithmically closed

Organically bound tritium

International Nuclear Information System (INIS)

Diabate, S.; Strack, S.

1993-01-01

Tritium released into the environment may be incorporated into organic matter. Organically bound tritium in that case will show retention times in organisms that are considerably longer than those of tritiated water which has significant consequences on dose estimates. This article reviews the most important processes of organically bound tritium production and transport through food networks. Metabolic reactions in plant and animal organisms with tritiated water as a reaction partner are of great importance in this respect. The most important production process, in quantitative terms, is photosynthesis in green plants. The translocation of organically bound tritium from the leaves to edible parts of crop plants should be considered in models of organically bound tritium behavior. Organically bound tritium enters the human body on several pathways, either from the primary producers (vegetable food) or at a higher tropic level (animal food). Animal experiments have shown that the dose due to ingestion of organically bound tritium can be up to twice as high as a comparable intake of tritiated water in gaseous or liquid form. In the environment, organically bound tritium in plants and animals is often found to have higher specific tritium concentrations than tissue water. This is not due to some tritium enrichment effects but to the fact that no equilibrium conditions are reached under natural conditions. 66 refs

Traveling-cluster approximation for uncorrelated amorphous systems

International Nuclear Information System (INIS)

Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.

1984-01-01

We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results

Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

CERN Document Server

Cornalba, L; Penedones, J; Schiappa, R; Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

2007-01-01

We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function _{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.

Physical Uncertainty Bounds (PUB)

Energy Technology Data Exchange (ETDEWEB)

Vaughan, Diane Elizabeth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Preston, Dean L. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-03-19

This paper introduces and motivates the need for a new methodology for determining upper bounds on the uncertainties in simulations of engineered systems due to limited fidelity in the composite continuum-level physics models needed to simulate the systems. We show that traditional uncertainty quantification methods provide, at best, a lower bound on this uncertainty. We propose to obtain bounds on the simulation uncertainties by first determining bounds on the physical quantities or processes relevant to system performance. By bounding these physics processes, as opposed to carrying out statistical analyses of the parameter sets of specific physics models or simply switching out the available physics models, one can obtain upper bounds on the uncertainties in simulated quantities of interest.

Modular structure of local algebras associated with massless free quantum fields

International Nuclear Information System (INIS)

Hislop, P.D.

1984-01-01

The Tomita modular operators and the duality property for the local von Neumann algebras in quantum field models describing free massless particles with arbitrary helicity are studied. It is proved that the representation of the Poincare group in each model extends to a unitary representation SU(2,2), a covering group of the conformal group. An irreducible set of standard linear fields is shown to be covariant with respect to this representation. The von Neumann algebras associated with wedge, double-cone, and lightcone regions generated by these fields are proved to be unitarily equivalent. Using the results of Bisognano and Wichmann, the modular operators for these algebras are obtained in explicit form as conformal transformations and the duality property is proved. In the bose case, it is shown that the double-cone algebras constructed from any irreducible set of linear fields not including the standard fields do not satisfy duality and that any non-standard linear fields are not conformally covariant. A simple proof of duality, independent of the Tomita-Takesaki theory, for the double-cone algebras in the scalar case is also presented

AdS3/CFT2, finite-gap equations and massless modes

International Nuclear Information System (INIS)

Lloyd, Thomas; Stefański, Bogdan Jr.

2014-01-01

It is known that string theory on AdS 3 ×M 7 backgrounds, where M 7 =S 3 ×S 3 ×S 1 or S 3 ×T 4 , is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finite-gap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finite-gap equations on these AdS 3 ×M 7 backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we re-examine the derivation of the AdS 3 ×M 7 finite-gap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finite-gap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS 3 ×M 7

Upper bounds on the relative energy difference of pure and mixed Gaussian states with a fixed fidelity

International Nuclear Information System (INIS)

Dodonov, V V

2012-01-01

Exact and approximate formulas for the upper bound of the relative energy difference of two Gaussian states with a fixed fidelity between them are derived. The reciprocal formulas for the upper bound of the fidelity for the fixed value of the relative energy difference are also obtained. The bounds appear higher for pure states than for mixed ones, and their maximal values correspond to squeezed vacuum states. In particular, to guarantee the relative energy difference less than 10%, for quite arbitrary Gaussian states, the fidelity between them must exceed the level 0.998866. (fast track communication)

Two-dimensional massless quantum electrodynamics in the Landau-gauge formalism and the Higgs mechanism. [Schwinger model

Energy Technology Data Exchange (ETDEWEB)

Ito, K R [Kyoto Univ. (Japan). Research Inst. for Mathematical Sciences

1975-03-01

The Schwinger model is considered in the Landau-gauge formalism of quantum electrodynamics. This model can be solved exactly on the assumption of no radiative corrections to the anomaly. It is found that the photon obtains a non-zero mass through the Higgs mechanism. In this case, the would-be Nambu-Goldstone boson is an associated boson which is constructed from a pair of two-component massless fermions. This would-be Nambu-Goldstone boson appears as a result of the spontaneous breaking of the gauge invariance of the first kind, and it becomes unphysical through the Higgs mechanism. However, as all the fermions themselves decouple from photons, they cannot appear as real particles in our world.

Localized bound states of fermions interacting via massive vector bosons

International Nuclear Information System (INIS)

Ionescu, D.C.; Reinhardt, J.; Mueller, B.; Greiner, W.; Soff, G.

1988-11-01

A model for composite consisting of fermions with internal degrees of freedom interacting via intermediate vector bosons (IVB) is constructed. We find highly localized, low-mass bound states in the Hartree-Fock approximation. We investigate the dependence of these states as function of the coupling constant and vector boson mass. In the limit of infinite vector boson mass the interaction is described by Fermi-type contact forces. (orig.)

On some applications of diophantine approximations.

Science.gov (United States)

Chudnovsky, G V

1984-03-01

Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to "almost all" numbers. In particular, any such number has the "2 + epsilon" exponent of irrationality: Theta - p/q > q(-2-epsilon) for relatively prime rational integers p,q, with q >/= q(0) (Theta, epsilon). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162].

Analytic result for the one-loop scalar pentagon integral with massless propagators

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Tarasov, Oleg V.

2010-01-01

The method of dimensional recurrences proposed by one of the authors (O. V.Tarasov, 1996) is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F 3 and the Gauss hypergeometric function 2 F 1 , both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions 2 F 1 . For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions 2 F 1 are presented in d=2-2ε, 4-2ε, and 6-2ε dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2ε dimensions is given in terms of the Appell function F 3 and the Gauss hypergeometric function 2 F 1 . (orig.)

Nonperturbative production of massless scalars during inflation and generation of gravitational waves

Energy Technology Data Exchange (ETDEWEB)

Goolsby-Cole, Cody; Sorbo, Lorenzo, E-mail: cgoolsby@physics.umass.edu, E-mail: sorbo@physics.umass.edu [Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, Amherst, MA, 01003 (United States)

2017-08-01

We discuss the possibility of a feature in the spectrum of inflationary gravitational waves sourced by a scalar field χ whose vacuum fluctuations are amplified by a rapidly time dependent mass. Unlike previous work which has focused on the case in which the mass of the field χ vanishes only for an instant before becoming massive again, we study a system where the scalar field becomes and remains massless through the end of inflation. After applying appropriate constraints to our parameters, we find, for future CMB experiments, a small contribution to the tensor-to-scalar ratio which can be at most of the order r ∼ 10{sup −5}. At smaller scales probed by gravitational interferometers, on the other hand, the energy density in the gravitational waves produced this way might be above the projected sensitivity of LISA, Ω{sub GW} h {sup 2} ∼ 10{sup −13}, in a narrow region of parameter space. If there is more than one χ species, then these amplitudes are enhanced by a factor equal to the number of those species.

Analytic result for the one-loop scalar pentagon integral with massless propagators

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Tarasov, Oleg V.

2010-01-01

The method of dimensional recurrences proposed by Tarasov (1996, 2000) is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F 3 and the Gauss hypergeometric function 2 F 1 , both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions 2 F 1 . For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions 2 F 1 are presented in d=2-2ε, 4-2ε, and 6-2ε dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2ε dimensions is given in terms of the Appell function F 3 and the Gauss hypergeometric function 2 F 1 .

Approximate solutions of common fixed-point problems

CERN Document Server

Zaslavski, Alexander J

2016-01-01

This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal...

Massless spectra and gauge couplings at one-loop on non-factorisable toroidal orientifolds

Science.gov (United States)

Berasaluce-González, Mikel; Honecker, Gabriele; Seifert, Alexander

2018-01-01

So-called 'non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al. [1] provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum - and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes - and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the Z4 × ΩR orientifolds on the A3 ×A1 ×B2-type torus. As observed before for factorisable backgrounds, also here the one-loop correction can drive the gauge groups to stronger coupling as demonstrated by means of a four-generation Pati-Salam example.

Polarized constituent quarks in NLO approximation

International Nuclear Information System (INIS)

Khorramian, Ali N.; Tehrani, S. Atashbar; Mirjalili, A.

2006-01-01

The valon representation provides a basis between hadrons and quarks, in terms of which the bound-state and scattering properties of hadrons can be united and described. We studied polarized valon distributions which have an important role in describing the spin dependence of parton distribution in leading and next-to-leading order approximation. Convolution integral in frame work of valon model as a useful tool, was used in polarized case. To obtain polarized parton distributions in a proton we need to polarized valon distribution in a proton and polarized parton distributions inside the valon. We employed Bernstein polynomial averages to get unknown parameters of polarized valon distributions by fitting to available experimental data

Bounds and Estimates for Transport Coefficients of Random and Porous Media with High Contrasts

International Nuclear Information System (INIS)

Berryman, J G

2004-01-01

Bounds on transport coefficients of random polycrystals of laminates are presented, including the well-known Hashin-Shtrikman bounds and some newly formulated bounds involving two formation factors for a two-component porous medium. Some new types of self-consistent estimates are then formulated based on the observed analytical structure both of these bounds and also of earlier self-consistent estimates (of the CPA or coherent potential approximation type). A numerical study is made, assuming first that the internal structure (i.e., the laminated grain structure) is not known, and then that it is known. The purpose of this aspect of the study is to attempt to quantify the differences in the predictions of properties of a system being modeled when such organized internal structure is present in the medium but detailed spatial correlation information may or (more commonly) may not be available. Some methods of estimating formation factors from data are also presented and then applied to a high-contrast fluid-permeability data set. Hashin-Shtrikman bounds are found to be very accurate estimates for low contrast heterogeneous media. But formation factor lower bounds are superior estimates for high contrast situations. The new self-consistent estimators also tend to agree better with data than either the bounds or the CPA estimates, which themselves tend to overestimate values for high contrast conducting composites

The strong running coupling from an approximate gluon Dyson-Schwinger equation

International Nuclear Information System (INIS)

Alkofer, R.; Hauck, A.

1996-01-01

Using Mandelstam's approximation to the gluon Dyson-Schwinger equation we calculate the gluon self-energy in a renormalisation group invariant fashion. We obtain a non-perturbative Β function. The scaling behavior near the ultraviolet stable fixed point is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found: α S increases without bound in the infrared

Bound states in quantum field theory and coherent states: A fresh look

International Nuclear Information System (INIS)

Misra, S.P.

1986-09-01

We consider here bound state equations in quantum field theory where the state explicitly includes radiation quanta as constituents with the number of such quanta not fixed. The fully interacting system is dealt with through equal time commutators/anticommutators of field operators. The multiparticle channel for the radiation field is approximated through coherent state representations. (author)

Four-body problem for four bound alpha particles in 16O

International Nuclear Information System (INIS)

Osman, A.

1980-02-01

The alpha cluster model is used in considering the 16 O nucleus as a bound state of four alpha particles. This problem is represented by integral equations which are exact effective two-particle equations. These equations have the form of two-particle Lippmann-Schwinger equations. The separable expressions are used in approximating the scattering amplitudes in the separable potential model to include also few and small non-separable rest parts of the interactions. The integral equations obtained are manageable and suitable for computations. Numerical calculations are carried out for the 16 O nucleus, with the structure of four bound alpha particles. The obtained binding energy of 16 O with that structure is 16.86 MeV which is in good agreement with the experimental value. (author)

78 FR 18326 - Agency Information Collection Activities; Comment Request; Upward Bound and Upward Bound Math...

Science.gov (United States)

2013-03-26

...; Comment Request; Upward Bound and Upward Bound Math Science Annual Performance Report AGENCY: The Office... considered public records. Title of Collection: Upward Bound and Upward Bound Math Science Annual Performance...) and Upward Bound Math and Science (UBMS) Programs. The Department is requesting a new APR because of...

Universal bounds on current fluctuations.

Science.gov (United States)

Pietzonka, Patrick; Barato, Andre C; Seifert, Udo

2016-05-01

For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.

Transformation of Black-Hole Hair under Duality and Supersymmetry

CERN Document Server

Alvarez, Enrique; Ortín, Tomas; Alvarez, Enrique; Meessen, Patrick; Ortin, Tomas

1997-01-01

We study the transformation under the String Theory duality group of the observable charges (mass, angular momentum, NUT charge, electric, magnetic and different scalar charges) of four dimensional point-like objects whose asymptotic behavior constitutes a subclass closed under duality. The charges fall into two complex four-dimensional representations of the duality group. T duality (including Buscher's) has an O(1,2) action on them and S duality a U(1) action. The generalized Bogomol'nyi bound is an U(2,2)-invariant built out of one representations while the other representation (which includes the angular momentum) never appears in it. The bound is manifestly duality-invariant. Consistency between T duality and supersymmetry requires that primary scalar hair is included in the Bogomol'nyi bound. Four-dimensional supersymmetric massless black holes are the T duals in time of massive supersymmetric black holes. Non-extreme massless ``black holes'' are the T duals of the non-extreme black holes and have prima...

Comparison of approximate methods for multiple scattering in high-energy collisions. II

International Nuclear Information System (INIS)

Nolan, A.M.; Tobocman, W.; Werby, M.F.

1976-01-01

The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

Science.gov (United States)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System

Science.gov (United States)

Goluskin, David

2018-04-01

We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be proved using Lyapunov functions. Nonnegativity is enforced by requiring the polynomials to be sums of squares, a condition which is then formulated as a semidefinite program (SDP) that can be solved computationally. Although such computations are subject to numerical error, we demonstrate two ways to obtain rigorous results: using interval arithmetic to control the error of an approximate SDP solution, and finding exact analytical solutions to relatively small SDPs. Previous formulations are extended to allow for bounds depending analytically on parametric variables. These methods are illustrated using the Lorenz equations, a system with three state variables ( x, y, z) and three parameters (β ,σ ,r). Bounds are reported for infinite-time averages of all eighteen moments x^ly^mz^n up to quartic degree that are symmetric under (x,y)\\mapsto (-x,-y). These bounds apply to all solutions regardless of stability, including chaotic trajectories, periodic orbits, and equilibrium points. The analytical approach yields two novel bounds that are sharp: the mean of z^3 can be no larger than its value of (r-1)^3 at the nonzero equilibria, and the mean of xy^3 must be nonnegative. The interval arithmetic approach is applied at the standard chaotic parameters to bound eleven average moments that all appear to be maximized on the shortest periodic orbit. Our best upper bound on each such average exceeds its value on the maximizing orbit by less than 1%. Many bounds reported here are much tighter than would be possible without computer assistance.

Rigorous upper bounds for transport due to passive advection by inhomogeneous turbulence

International Nuclear Information System (INIS)

Krommes, J.A.; Smith, R.A.

1987-05-01

A variational procedure, due originally to Howard and explored by Busse and others for self-consistent turbulence problems, is employed to determine rigorous upper bounds for the advection of a passive scalar through an inhomogeneous turbulent slab with arbitrary generalized Reynolds number R and Kubo number K. In the basic version of the method, the steady-state energy balance is used as a constraint; the resulting bound, though rigorous, is independent of K. A pedagogical reference model (one dimension, K = ∞) is described in detail; the bound compares favorably with the exact solution. The direct-interaction approximation is also worked out for this model; it is somewhat more accurate than the bound, but requires considerably more labor to solve. For the basic bound, a general formalism is presented for several dimensions, finite correlation length, and reasonably general boundary conditions. Part of the general method, in which a Green's function technique is employed, applies to self-consistent as well as to passive problems, and thereby generalizes previous results in the fluid literature. The formalism is extended for the first time to include time-dependent constraints, and a bound is deduced which explicitly depends on K and has the correct physical scalings in all regimes of R and K. Two applications from the theory of turbulent plasmas ae described: flux in velocity space, and test particle transport in stochastic magnetic fields. For the velocity space problem the simplest bound reproduces Dupree's original scaling for the strong turbulence diffusion coefficient. For the case of stochastic magnetic fields, the scaling of the bounds is described for the magnetic diffusion coefficient as well as for the particle diffusion coefficient in the so-called collisionless, fluid, and double-streaming regimes

Quivers of Bound Path Algebras and Bound Path Coalgebras

Directory of Open Access Journals (Sweden)

Dr. Intan Muchtadi

2010-09-01

Full Text Available bras and coalgebras can be represented as quiver (directed graph, and from quiver we can construct algebras and coalgebras called path algebras and path coalgebras. In this paper we show that the quiver of a bound path coalgebra (resp. algebra is the dual quiver of its bound path algebra (resp. coalgebra.

Regularization of a massless dirac model to describe anomalous electromagnetic response of Weyl semimetals

International Nuclear Information System (INIS)

Takane, Yoshitake

2016-01-01

An unbounded massless Dirac model with two nondegenerate Dirac cones is the simplest model for Weyl semimetals, which show the anomalous electromagnetic response of chiral magnetic effect (CME) and anomalous Hall effect (AHE). However, if this model is naively used to analyze the electromagnetic response within a linear response theory, it gives the result apparently inconsistent with the persuasive prediction based on a lattice model. We show that this serious difficulty is related to the breaking of current conservation in the Dirac model due to quantum anomaly and can be removed if current and charge operators are redefined to include the contribution from the anomaly. We demonstrate that the CME as well as the AHE can be properly described using newly defined operators, and clarify that the CME is determined by the competition between the contribution from the anomaly and that from low-energy electrons. (author)

Scattering of massless particles: scalars, gluons and gravitons

Science.gov (United States)

Cachazo, Freddy; He, Song; Yuan, Ellis Ye

2014-07-01

In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of n marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U( N ) color structures while the second is a Pfaffian. The S-matrix of a U( N ) × U( Ñ ) cubic scalar theory is obtained by simply replacing the Pfaffian with a U( Ñ ) version of the previous U( N ) factor. Given that gravity amplitudes are obtained by replacing the U( N ) factor in Yang-Mills by a second Pfaffian, we are led to a natural color-kinematics correspondence. An expansion of the integrand of the scalar theory leads to sums over trivalent graphs and are directly related to the KLT matrix. Combining this and the Yang-Mills formula we find a connection to the BCJ color-kinematics duality as well as a new proof of the BCJ doubling property that gives rise to gravity amplitudes. We end by considering a special kinematic point where the partial amplitude simply counts the number of color-ordered planar trivalent trees, which equals a Catalan number. The scattering equations simplify dramatically and are equivalent to a special Y-system with solutions related to roots of Chebyshev polynomials. The sum of the integrand over the solutions gives rise to a representation of Catalan numbers in terms of eigenvectors and eigenvalues of the adjacency matrix of an A-type Dynkin diagram.

Photon virtual bound state

International Nuclear Information System (INIS)

Inoue, J.; Ohtaka, K.

2004-01-01

We study virtual bound states in photonics, which are a vectorial extension of electron virtual bound states. The condition for these states is derived. It is found that the Mie resonant state which satisfies the condition that the size parameter is less than the angular momentum should be interpreted as a photon virtual bound state. In order to confirm the validity of the concept, we compare the photonic density of states, the width of which represents the lifetime of the photon virtual bound states, with numerical results

Monopole-fermion and dyon-fermion bound states. Pt. 5

International Nuclear Information System (INIS)

Osland, P.; Harvard Univ., Cambridge, MA; Schultz, C.L.; Wu, T.T.

1985-02-01

We present explicit, approximate, remarkably precise results for the Kazama-Yang hamiltonian, which describes a Dirac monopole interacting with a spin-1/2 fermion that has an extra magnetic moment. The results are valid for bound states of angular momentum j >= Zvertical strokeegvertical stroke+1/2, where the radial wave functions are determined by four coupled differential equations. These equations have been solved analytically for M - E << M, which is a limit of considerable practical interest. Binding energies and wave functions are given. (orig.)

Solvable light-front model of the electromagnetic form factor of the relativistic two-body bound state in 1+1 dimensions

International Nuclear Information System (INIS)

Mankiewicz, L.; Sawicki, M.

1989-01-01

Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics

Extended particle model with quark confinement and charmonium spectroscopy

International Nuclear Information System (INIS)

Hasenfratz, Peter; Kuti, Julius; Szalay, A.S.

Extended particle like vector gluon bubbles /bags/ are introduced which are stabilized against free expansion by a surface tension of volume tension. Since quraks are coupled to the gluon field, they are confined to the inside of the gluon bag without any further mechanism. Only color singlet gluon bags are allowed. Nonlinear boundary conditions are not imposed on the quark field in the model. A massless abelian gauge confined by a surface tension is first considered; in a four-dimensional relativistic picture the surface of the gauge field bubble appears as a tube with a three dimensional surface. As a first application, the model is used to study bound states of heavy charmed quarks (charmonium). Similar to the Born-Oppenheimer approximation in molecular physics, heavy charmed quarks are treated as nonrelativistic in their motion whereas the gluon bag and light quarks (u,d,s) are treated in an adiabatic approximation

First error bounds for the porous media approximation of the Poisson-Nernst-Planck equations

Energy Technology Data Exchange (ETDEWEB)

Schmuck, Markus [Imperial College, London (United Kingdom). Depts. of Chemical Engineering and Mathematics

2012-04-15

We study the well-accepted Poisson-Nernst-Planck equations modeling transport of charged particles. By formal multiscale expansions we rederive the porous media formulation obtained by two-scale convergence in [42, 43]. The main result is the derivation of the error which occurs after replacing a highly heterogeneous solid-electrolyte composite by a homogeneous one. The derived estimates show that the approximation errors for both, the ion densities quantified in L{sup 2}-norm and the electric potential measured in H{sup 1}-norm, are of order O(s{sup 1/2}). (orig.)

Space-Efficient Approximation Scheme for Circular Earth Mover Distance

DEFF Research Database (Denmark)

Brody, Joshua Eric; Liang, Hongyu; Sun, Xiaoming

2012-01-01

The Earth Mover Distance (EMD) between point sets A and B is the minimum cost of a bipartite matching between A and B. EMD is an important measure for estimating similarities between objects with quantifiable features and has important applications in several areas including computer vision...... to computer vision [13] and can be seen as a special case of computing EMD on a discretized grid. We achieve a (1 ±ε) approximation for EMD in $\\tilde O(\\varepsilon^{-3})$ space, for every 0 ... that matches the space bound asked in [9]....

Approximate Dual Averaging Method for Multiagent Saddle-Point Problems with Stochastic Subgradients

Directory of Open Access Journals (Sweden)

Deming Yuan

2014-01-01

Full Text Available This paper considers the problem of solving the saddle-point problem over a network, which consists of multiple interacting agents. The global objective function of the problem is a combination of local convex-concave functions, each of which is only available to one agent. Our main focus is on the case where the projection steps are calculated approximately and the subgradients are corrupted by some stochastic noises. We propose an approximate version of the standard dual averaging method and show that the standard convergence rate is preserved, provided that the projection errors decrease at some appropriate rate and the noises are zero-mean and have bounded variance.

Analytic result for the one-loop scalar pentagon integral with massless propagators

Energy Technology Data Exchange (ETDEWEB)

Kniehl, Bernd A.; Tarasov, Oleg V. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

2010-01-15

The method of dimensional recurrences proposed by one of the authors (O. V.Tarasov, 1996) is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F{sub 3} and the Gauss hypergeometric function {sub 2}F{sub 1}, both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions {sub 2}F{sub 1}. For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions {sub 2}F{sub 1} are presented in d=2-2{epsilon}, 4-2{epsilon}, and 6-2{epsilon} dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2{epsilon} dimensions is given in terms of the Appell function F{sub 3} and the Gauss hypergeometric function {sub 2}F{sub 1}. (orig.)

Spermidine is bound to a unique protein in early sea urchin embryos

International Nuclear Information System (INIS)

Canellakis, Z.N.; Bondy, P.K.; Infante, A.A.

1985-01-01

Spermidine is rapidly taken up and becomes bound to protein during the very early hours of sea urchin embryogenesis. During the first 6 hr after fertilization of freshly obtained sea urchin eggs (Strongylocentrotus purpuratus), which are incubated in the presence of exogenous [ 3 H]-spermidine, up to 7% of the total cell-associated spermidine appears uniquely as spermidine bound in macromolecular form. This unique protein containing spermidine migrates as a single radioactive band in gel electrophoresis. It has a Mr of approximately equal to 30,000 and is readily distinguishable from the protein initiation factor eIF-4D, which has a Mr of 18,000, the only other identifiable protein known to date to be posttranslationally modified by polyamines

$O(N)$ model in Euclidean de Sitter space: beyond the leading infrared approximation

CERN Document Server

Nacir, Diana López; Trombetta, Leonardo G

2016-01-01

We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the $O(N)$ theory a systematic method introduced previously for a single field, which treats the zero modes exactly and the nonzero modes perturbatively. We compute the two-point functions taking into account not only the leading infrared contribution, coming from the self-interaction of the zero modes, but also corrections due to the interaction of the ultraviolet modes. For the model defined in the corresponding Lorentzian de Sitter spacetime, we obtain the two-point functions by analytical continuation. We point out that a partial resummation of the leading secular terms (which necessarily involves nonzero modes) is required to obtain a decay at large distances for massless fields. We implement this resummation along with a systematic double expansion in an effective coupling c...

The boundary-corrected second Born (B2B) approximation: proton-hydrogen electron capture

International Nuclear Information System (INIS)

Dewangan, D.P.; Bransden, B.H.

1988-01-01

The probability amplitude for proton-hydrogen ground-state electron capture at 125 keV in the boundary-corrected second Born approximation has been evaluated numerically by retaining all significant bound and continuum hydrogenic intermediate states for which the orbital angular momentum l ≤ 3. The differential cross section is found to be in good agreement with the experimental data for scattering angles less than about 1 mrad in the centre of mass system. The value of the boundary-corrected second Born total cross section is similar to that obtained in the boundary-corrected first Born approximation. (author)

Analyticity of effective coupling and propagators in massless models of quantum field theory

International Nuclear Information System (INIS)

Oehme, R.

1982-01-01

For massless models of quantum field theory, some general theorems are proved concerning the analytic continuation of the renormalization group functions as well as the effective coupling and the propagators. Starting points are analytic properties of the effective coupling and the propagators in the momentum variable k 2 , which can be converted into analyticity of β- and γ-functions in the coupling parameter lambda. It is shown that the β-function can have branch point singularities related to stationary points of the effective coupling as a function of k 2 . The type of these singularities of β(lambda) can be determined explicitly. Examples of possible physical interest are extremal values of the effective coupling at space-like points in the momentum variable, as well as complex conjugate stationary points close to the real k 2 -axis. The latter may be related to the sudden transition between weak and strong coupling regimes of the system. Finally, for the effective coupling and for the propagators, the analytic continuation in both variables k 2 and lambda is discussed. (orig.)

Influence of retardation effects on photodisintegration of a quantum system bound by short-range forces

International Nuclear Information System (INIS)

Preobrazhenskii, M.A.; Golovinskii, P.A.

1996-01-01

Expressions for cross sections for multiphonon disintegration of quantum systems bound by short-range forces are obtained in the plane-wave approximation taking into account retardation effects. It is shown that, in the region of nonrelativistic energies, their contribution is factored, and the resulting universal factor is expressed for an arbitrary degree of process nonlinearity n in terms of elementary functions. Arguments of functions are determined only by the mode ω, the radiation spectrum width β, and the bound-state energy of a system. The dependence of the contribution of retardation effects on ω, β, and n is studied in detail. Analytical expressions for cross sections for multiquantum disintegration in the first nonvanishing order with respect to correlation interaction, which exactly take into account retardation effects, are obtained. It is shown that for two-quantum processes, the contribution of correlation effects is expressed in terms of a function representing an extension of dipole polarizability, whereas for n>2, it can be described in the dipole approximation

An interval-valued reliability model with bounded failure rates

DEFF Research Database (Denmark)

Kozine, Igor; Krymsky, Victor

2012-01-01

The approach to deriving interval-valued reliability measures described in this paper is distinctive from other imprecise reliability models in that it overcomes the issue of having to impose an upper bound on time to failure. It rests on the presupposition that a constant interval-valued failure...... rate is known possibly along with other reliability measures, precise or imprecise. The Lagrange method is used to solve the constrained optimization problem to derive new reliability measures of interest. The obtained results call for an exponential-wise approximation of failure probability density...

Bounds on the number of bound states in the transfer matrix spectrum for some weakly correlated lattice models

International Nuclear Information System (INIS)

O’Carroll, Michael

2012-01-01

We consider the interaction of particles in weakly correlated lattice quantum field theories. In the imaginary time functional integral formulation of these theories there is a relative coordinate lattice Schroedinger operator H which approximately describes the interaction of these particles. Scalar and vector spin, QCD and Gross-Neveu models are included in these theories. In the weakly correlated regime H=H o +W where H o =−γΔ l , 0 l is the d-dimensional lattice Laplacian: γ=β, the inverse temperature for spin systems and γ=κ 3 where κ is the hopping parameter for QCD. W is a self-adjoint potential operator which may have non-local contributions but obeys the bound ‖W(x, y)‖⩽cexp ( −a(‖x‖+‖y‖)), a large: exp−a=β/β o (1/2) (κ/κ o ) for spin (QCD) models. H o , W, and H act in l 2 (Z d ), d⩾ 1. The spectrum of H below zero is known to be discrete and we obtain bounds on the number of states below zero. This number depends on the short range properties of W, i.e., the long range tail does not increase the number of states.

Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

International Nuclear Information System (INIS)

Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo

2007-01-01

We introduce the impact parameter representation for conformal field theory correlators of the form A∼ 1 O 2 O 1 O 2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function 1 O 1 > shock in the presence of a shock wave in anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling

Stability of a nonlinear second order equation under parametric bounded noise excitation

International Nuclear Information System (INIS)

Wiebe, Richard; Xie, Wei-Chau

2016-01-01

The motivation for the following work is a structural column under dynamic axial loads with both deterministic (harmonic transmitted forces from the surrounding structure) and random (wind and/or earthquake) loading components. The bounded noise used herein is a sinusoid with an argument composed of a random (Wiener) process deviation about a mean frequency. By this approach, a noise parameter may be used to investigate the behavior through the spectrum from simple harmonic forcing, to a bounded random process with very little harmonic content. The stability of both the trivial and non-trivial stationary solutions of an axially-loaded column (which is modeled as a second order nonlinear equation) under parametric bounded noise excitation is investigated by use of Lyapunov exponents. Specifically the effect of noise magnitude, amplitude of the forcing, and damping on stability of a column is investigated. First order averaging is employed to obtain analytical approximations of the Lyapunov exponents of the trivial solution. For the non-trivial stationary solution however, the Lyapunov exponents are obtained via Monte Carlo simulation as the stability equations become analytically intractable. (paper)

Curvature bound from gravitational catalysis

Science.gov (United States)

Gies, Holger; Martini, Riccardo

2018-04-01

We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.

Dilation volumes of sets of bounded perimeter

DEFF Research Database (Denmark)

Kiderlen, Markus; Rataj, Jan

, this derivative coincides up to sign with the directional derivative of the covariogram of A in direction u. By known results for the covariogram, this derivative can therefore be expressed by the cosine transform of the surface area measure of A. We extend this result to sets Q that are at most countable and use...... it to determine the derivative of the contact distribution function of a stationary random closed set at zero. A variant for uncountable Q is given, too. The proofs are based on approximation of the characteristic function of A by smooth functions of bounded variation and showing corresponding formulas for them....

Lognormal Approximations of Fault Tree Uncertainty Distributions.

Science.gov (United States)

El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P

2018-01-26

Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.

Deeply bound pionic atom

International Nuclear Information System (INIS)

Toki, Hiroshi; Yamazaki, Toshimitsu

1989-01-01

The standard method of pionic atom formation does not produce deeply bound pionic atoms. A study is made on the properties of deeply bound pionic atom states by using the standard pion-nucleus optical potential. Another study is made to estimate the cross sections of the formation of ls pionic atom states by various methods. The pion-nucleus optical potential is determined by weakly bound pionic atom states and pion nucleus scattering. Although this potential may not be valid for deeply bound pionic atoms, it should provide some hint on binding energies and level widths of deeply bound states. The width of the ls state comes out to be 0.3 MeV and is well separated from the rest. The charge dependence of the ls state is investigated. The binding energies and the widths increase linearly with Z azbove a Z of 30. The report then discusses various methods to populate deeply bound pionic atoms. In particular, 'pion exchange' reactions are proposed. (n, pπ) reaction is discussed first. The cross section is calculated by assuming the in- and out-going nucleons on-shell and the produced pion in (n1) pionic atom states. Then, (n, dπ - ) cross sections are estimated. (p, 2 Heπ - ) reaction would have cross sections similar to the cross section of (n, dπ - ) reaction. In conclusion, it seems best to do (n, p) experiment on heavy nuclei for deeply bound pionic atom. (Nogami, K.)

Analysis of a Cartesian PML approximation to acoustic scattering problems in and

KAUST Repository

Bramble, James H.

2013-08-01

We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.

Bounding species distribution models

Directory of Open Access Journals (Sweden)

Thomas J. STOHLGREN, Catherine S. JARNEVICH, Wayne E. ESAIAS,Jeffrey T. MORISETTE

2011-10-01

Full Text Available Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for “clamping” model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART and maximum entropy (Maxent models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5: 642–647, 2011].

Bounding Species Distribution Models

Science.gov (United States)

Stohlgren, Thomas J.; Jarnevich, Cahterine S.; Morisette, Jeffrey T.; Esaias, Wayne E.

2011-01-01

Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647, 2011].

Is there a lower bound energy in the harmonic oscillator interacting with a heat bath?

International Nuclear Information System (INIS)

Arevalo Aguilar, L.M.; Almeida, N.G. de; Villas-Boas, C.J.

2003-01-01

In this Letter we investigate the lower bound energy of the usual Hamiltonian employed in Quantum Optics to model the interaction between a harmonic oscillator and a reservoir without the rotating wave approximation. We show that this model has serious inconsistencies and then we discuss the origin of these inconsistencies

Diffraction scattering of strongly bound system

International Nuclear Information System (INIS)

Kuzmichev, V.E.

1982-04-01

The scattering of a hadron on a strongly bound system of two hadrons (dihadron) is considered in the high-energy limit for the relative hadron-dihadron motion. The dihadron scatterer motion and the internal interaction are included in our consideration. It is shown that only small values of the internal transfer momentum of dihadron particles bring the principal contribution to the three-particle propagator in eikonal approximation. On the basis of the exact analytical solution of the integral equation for the total Green function the scattering amplitude is derived. It is shown that the scattering amplitude contains only single, double, and triple scattering terms. The three new terms to the Glauber formula for the total cross section are obtained. These terms decrease both the true total hadron-hadron cross section and the screening correction. (orig.)

Lower complexity bounds for lifted inference

DEFF Research Database (Denmark)

Jaeger, Manfred

2015-01-01

instances of the model. Numerous approaches for such “lifted inference” techniques have been proposed. While it has been demonstrated that these techniques will lead to significantly more efficient inference on some specific models, there are only very recent and still quite restricted results that show...... the feasibility of lifted inference on certain syntactically defined classes of models. Lower complexity bounds that imply some limitations for the feasibility of lifted inference on more expressive model classes were established earlier in Jaeger (2000; Jaeger, M. 2000. On the complexity of inference about...... that under the assumption that NETIME≠ETIME, there is no polynomial lifted inference algorithm for knowledge bases of weighted, quantifier-, and function-free formulas. Further strengthening earlier results, this is also shown to hold for approximate inference and for knowledge bases not containing...

Statistical validation of engineering and scientific models : bounds, calibration, and extrapolation.

Energy Technology Data Exchange (ETDEWEB)

Dowding, Kevin J.; Hills, Richard Guy (New Mexico State University, Las Cruces, NM)

2005-04-01

Numerical models of complex phenomena often contain approximations due to our inability to fully model the underlying physics, the excessive computational resources required to fully resolve the physics, the need to calibrate constitutive models, or in some cases, our ability to only bound behavior. Here we illustrate the relationship between approximation, calibration, extrapolation, and model validation through a series of examples that use the linear transient convective/dispersion equation to represent the nonlinear behavior of Burgers equation. While the use of these models represents a simplification relative to the types of systems we normally address in engineering and science, the present examples do support the tutorial nature of this document without obscuring the basic issues presented with unnecessarily complex models.

Diophantine approximation and badly approximable sets

DEFF Research Database (Denmark)

Kristensen, S.; Thorn, R.; Velani, S.

2006-01-01

. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

Labeling schemes for bounded degree graphs

DEFF Research Database (Denmark)

Adjiashvili, David; Rotbart, Noy Galil

2014-01-01

We investigate adjacency labeling schemes for graphs of bounded degree Δ = O(1). In particular, we present an optimal (up to an additive constant) log n + O(1) adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar...... graphs. Our results complement a similar bound recently obtained for bounded depth trees [Fraigniaud and Korman, SODA 2010], and may provide new insights for closing the long standing gap for adjacency in trees [Alstrup and Rauhe, FOCS 2002]. We also provide improved labeling schemes for bounded degree...

The interplay of intrinsic and extrinsic bounded noises in biomolecular networks.

Directory of Open Access Journals (Sweden)

Giulio Caravagna

Full Text Available After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: (i the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, (ii a model of enzymatic futile cycle and (iii a genetic toggle switch. In (ii and (iii we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.

The interplay of intrinsic and extrinsic bounded noises in biomolecular networks.

Science.gov (United States)

Caravagna, Giulio; Mauri, Giancarlo; d'Onofrio, Alberto

2013-01-01

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: (i) the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, (ii) a model of enzymatic futile cycle and (iii) a genetic toggle switch. In (ii) and (iii) we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.

Improved bounds on the epidemic threshold of exact SIS models on complex networks

KAUST Repository

Ruhi, Navid Azizan; Thrampoulidis, Christos; Hassibi, Babak

2017-01-01

The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.

Improved bounds on the epidemic threshold of exact SIS models on complex networks

KAUST Repository

Ruhi, Navid Azizan

2017-01-05

The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network\\'s adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.

Gauge-invariant, nonperturbative approach to the infrared-finite bound-state problem in QCD

International Nuclear Information System (INIS)

Gogokhia, V.Sh.

1989-09-01

Gauge invariant, nonperturbative approach to the bound state problem within the infrared finite Bethe-Salpeter equation is presented. Condition of cancellation of the nonperturbative infrared divergences is derived. Solutions for the quark propagator and corresponding quark gluon vertex function are written down which can be directly applied to the Bethe-Salpeter equation, in particular to the 'generalized ladder' approximation of this equation. (author) 18 refs.; 3 figs

Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach

KAUST Repository

Collier, Nathan

2011-05-14

We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.

bb̅ud̅ four-quark systems in the Born-Oppenheimer approximation: prospects and challenges

Science.gov (United States)

Peters, Antje; Bicudo, Pedro; Wagner, Marc

2018-03-01

We summarize previous work on b̅b̅ud four-quark systems in the Born-Oppenheimer approximation and discuss first steps towards an extension to the theoretically more challenging bb̅ud̅ system. Strategies to identify a possibly existing bb̅ud̅ bound state are discussed and first numerical results are presented.

Calculation of field configurations of the electrostatic septum and massless septum magnet for the slow extraction system of the JHF main ring

International Nuclear Information System (INIS)

Watanabe, Tamaki; Tokuda, Noboru; Tomizawa, Masahito; Arakaki, Yoshitsugu; Machida, Shinji; Mori, Yoshiharu; Shibuya, Shinji

1997-01-01

Since accelerating beam intensity is enormous in the JHF synchrotron, even small beam losses during the slow extraction leads to unacceptable level of radiation. We set a criterion such that tolerable beam loss in the slow extraction process should be less than 1% of the averaged beam current of 10 μA. We have examined the field configurations of the electrostatic septum and the massless septum magnet, respectively. The calculations of electrostatic and magnetic fields were carried out by the computer code POISSON. (author)

The Cramér-Rao Bounds and Sensor Selection for Nonlinear Systems with Uncertain Observations.

Science.gov (United States)

Wang, Zhiguo; Shen, Xiaojing; Wang, Ping; Zhu, Yunmin

2018-04-05

This paper considers the problems of the posterior Cramér-Rao bound and sensor selection for multi-sensor nonlinear systems with uncertain observations. In order to effectively overcome the difficulties caused by uncertainty, we investigate two methods to derive the posterior Cramér-Rao bound. The first method is based on the recursive formula of the Cramér-Rao bound and the Gaussian mixture model. Nevertheless, it needs to compute a complex integral based on the joint probability density function of the sensor measurements and the target state. The computation burden of this method is relatively high, especially in large sensor networks. Inspired by the idea of the expectation maximization algorithm, the second method is to introduce some 0-1 latent variables to deal with the Gaussian mixture model. Since the regular condition of the posterior Cramér-Rao bound is unsatisfied for the discrete uncertain system, we use some continuous variables to approximate the discrete latent variables. Then, a new Cramér-Rao bound can be achieved by a limiting process of the Cramér-Rao bound of the continuous system. It avoids the complex integral, which can reduce the computation burden. Based on the new posterior Cramér-Rao bound, the optimal solution of the sensor selection problem can be derived analytically. Thus, it can be used to deal with the sensor selection of a large-scale sensor networks. Two typical numerical examples verify the effectiveness of the proposed methods.

A risk standard based on societal cost with bounded consequences

International Nuclear Information System (INIS)

Worledge, D.H.

1982-01-01

A risk standard is proposed that relates the frequency of occurrence of single events to the consequences of the events. Maximum consequences and risk aversion are used to give the cumulative risk curve a shape similar to the results of a risk assessment and to bound the expectation of deaths. Societal costs in terms of deaths are used to fix the parameters of the model together with an approximate comparison with individual risks. The proposed standard is compared with some practical applications of risk assessment to nuclear reactor systems

Scattering by bound nucleons

International Nuclear Information System (INIS)

Tezuka, Hirokazu.

1984-10-01

Scattering of a particle by bound nucleons is discussed. Effects of nucleons that are bound in a nucleus are taken as a structure function. The way how to calculate the structure function is given. (author)

Market access through bound tariffs

DEFF Research Database (Denmark)

Sala, Davide; Yalcin, Erdal; Schröder, Philipp

2010-01-01

on the risk that exporters face in destination markets. The present paper formalizes the underlying interaction of risk, fixed export costs and firms' market entry decisions based on techniques known from the real options literature; doing so we highlight the important role of bound tariffs at the extensive...... margin of trade. We find that bound tariffs are more effective with higher risk destination markets, that a large binding overhang may still command substantial market access, and that reductions in bound tariffs generate effective market access even when bound rates are above current and longterm...

Market Access through Bound Tariffs

DEFF Research Database (Denmark)

Sala, Davide; Schröder, Philipp J.H.; Yalcin, Erdal

on the risk that exporters face in destination markets. The present paper formalizes the underlying interaction of risk, fixed export costs and firms' market entry decisions based on techniques known from the real options literature; doing so we highlight the important role of bound tariffs at the extensive...... margin of trade. We find that bound tariffs are more effective with higher risk destination markets, that a large binding overhang may still command substantial market access, and that reductions in bound tariffs generate effective market access even when bound rates are above current and long...

Exploring L1 model space in search of conductivity bounds for the MT problem

Science.gov (United States)

Wheelock, B. D.; Parker, R. L.

2013-12-01

Geophysical inverse problems of the type encountered in electromagnetic techniques are highly non-unique. As a result, any single inverted model, though feasible, is at best inconclusive and at worst misleading. In this paper, we use modified inversion methods to establish bounds on electrical conductivity within a model of the earth. Our method consists of two steps, each making use of the 1-norm in model regularization. Both 1-norm minimization problems are framed without approximation as non-negative least-squares (NNLS) problems. First, we must identify a parsimonious set of regions within the model for which upper and lower bounds on average conductivity will be sought. This is accomplished by minimizing the 1-norm of spatial variation, which produces a model with a limited number of homogeneous regions; in fact, the number of homogeneous regions will never be greater than the number of data, regardless of the number of free parameters supplied. The second step establishes bounds for each of these regions with pairs of inversions. The new suite of inversions also uses a 1-norm penalty, but applied to the conductivity values themselves, rather than the spatial variation thereof. In the bounding step we use the 1-norm of our model parameters because it is proportional to average conductivity. For a lower bound on average conductivity, the 1-norm within a bounding region is minimized. For an upper bound on average conductivity, the 1-norm everywhere outside a bounding region is minimized. The latter minimization has the effect of concentrating conductance into the bounding region. Taken together, these bounds are a measure of the uncertainty in the associated region of our model. Starting with a blocky inverse solution is key in the selection of the bounding regions. Of course, there is a tradeoff between resolution and uncertainty: an increase in resolution (smaller bounding regions), results in greater uncertainty (wider bounds). Minimization of the 1-norm of

Production of massless bottom jets in p anti p and pp collisions at next-to-leading order of QCD

International Nuclear Information System (INIS)

Bierenbaum, Isabella; Kramer, Gustav

2016-03-01

We present predictions for the inclusive production of bottom jets in proton-antiproton collisions at 1.96 TeV and proton-proton collisions at 7 TeV. The bottom quark is considered massless. In this scheme, we find that at small transverse momentum (p T ) the ratio of the next-to-leading order to the leading-order cross section (K factor) is smaller than one. It increases with increasing p T and approaches one at larger p T at a value depending essentially on the choice of the renormalization scale. Adding non-perturbative corrections obtained from PYTHIA Monte Carlo calculations leads to reasonable agreement with experimental b-jet cross sections obtained by the CDF and the CMS collaborations.

A S-matrix-like approximation in the charged particle scattering by the hydrogen atom

International Nuclear Information System (INIS)

Mignaco, J.A.; Tort, A.C.

1979-01-01

The Born approximation for charged particle scattering by the hydrogen atom is unfit at low energies. From a S-matrix-like consideration on the dominance of the neighbour singularities, the calculation of other contributions is suggested. The inclusion of bound states is made, following Eden's and his colaborators' ideas, which are described by their interest and likeness with procedures in the intermediate energy physics. (Author) [pt

Computing gap free Pareto front approximations with stochastic search algorithms.

Science.gov (United States)

Schütze, Oliver; Laumanns, Marco; Tantar, Emilia; Coello, Carlos A Coello; Talbi, El-Ghazali

2010-01-01

Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of epsilon-dominance. Though bounds on the quality of the limit approximation-which are entirely determined by the archiving strategy and the value of epsilon-have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a epsilon A, is "large." Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy-multi-objective continuation methods-by showing that the concept of epsilon-dominance can be integrated into this approach in a suitable way.

A Sobolev-Type Upper Bound for Rates of Approximation by Linear Combinations of Heaviside Plane Waves

Czech Academy of Sciences Publication Activity Database

Kainen, P.C.; Kůrková, Věra; Vogt, A.

2007-01-01

Roč. 147, č. 1 (2007), s. 1-10 ISSN 0021-9045 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10300504 Keywords : characteristic functions of closed half-spaces * perceptron neural networks * integral formulas * variation with respect to half-spaces * Radon transform * Gaussian function * rates of approximation Subject RIV: IN - Informatics, Computer Science Impact factor: 0.697, year: 2007

Deeply quasi-bound state in single- and double-K nuclear clusters

Energy Technology Data Exchange (ETDEWEB)

Marri, S.; Kalantari, S.Z. [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Esmaili, J. [Shahrekord University, Department of Physics, Faculty of Basic Sciences, Shahrekord (Iran, Islamic Republic of)

2016-12-15

New calculations of the quasi-bound state positions in K{sup -}K{sup -}pp kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three- and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models of anti KN-πΣ potentials with one- and two-pole structure of Λ(1405) resonance and separable potential models for anti K- anti K and nucleon-nucleon interactions, are used. The dependence of the resulting four-body binding energy on models of anti KN-πΣ interaction is investigated. We obtained the binding energy of the K{sup -}K{sup -}pp quasi-bound state ∝ 80-94 MeV with the phenomenological anti KN potentials. The width is about ∝ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give ∝ 24-31 MeV width. (orig.)

Approximate labeling via graph cuts based on linear programming.

Science.gov (United States)

Komodakis, Nikos; Tziritas, Georgios

2007-08-01

A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems.

Metabolism of organically bound tritium

International Nuclear Information System (INIS)

Travis, C.C.

1984-01-01

The classic methodology for estimating dose to man from environmental tritium ignores the fact that organically bound tritium in foodstuffs may be directly assimilated in the bound compartment of tissues without previous oxidation. We propose a four-compartment model consisting of a free body water compartment, two organic compartments, and a small, rapidly metabolizing compartment. The utility of this model lies in the ability to input organically bound tritium in foodstuffs directly into the organic compartments of the model. We found that organically bound tritium in foodstuffs can increase cumulative total body dose by a factor of 1.7 to 4.5 times the free body water dose alone, depending on the bound-to-loose ratio of tritium in the diet. Model predictions are compared with empirical measurements of tritium in human urine and tissue samples, and appear to be in close agreement. 10 references, 4 figures, 3 tables

Bound states in string nets

Science.gov (United States)

Schulz, Marc Daniel; Dusuel, Sébastien; Vidal, Julien

2016-11-01

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

Science.gov (United States)

Choi, Yun Ho; Yoo, Sung Jin

2017-03-28

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Bounding approaches to system identification

CERN Document Server

Norton, John; Piet-Lahanier, Hélène; Walter, Éric

1996-01-01

In response to the growing interest in bounding error approaches, the editors of this volume offer the first collection of papers to describe advances in techniques and applications of bounding of the parameters, or state variables, of uncertain dynamical systems. Contributors explore the application of the bounding approach as an alternative to the probabilistic analysis of such systems, relating its importance to robust control-system design.

Bounds for percolation thresholds on directed and undirected graphs

Science.gov (United States)

Hamilton, Kathleen; Pryadko, Leonid

2015-03-01

Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.

Bounded Intention Planning Revisited

OpenAIRE

Sievers Silvan; Wehrle Martin; Helmert Malte

2014-01-01

Bounded intention planning provides a pruning technique for optimal planning that has been proposed several years ago. In addition partial order reduction techniques based on stubborn sets have recently been investigated for this purpose. In this paper we revisit bounded intention planning in the view of stubborn sets.

Bounded Gaussian process regression

DEFF Research Database (Denmark)

Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan

2013-01-01

We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...... with the proposed explicit noise-model extension....

A symmetric Roos bound for linear codes

NARCIS (Netherlands)

Duursma, I.M.; Pellikaan, G.R.

2006-01-01

The van Lint–Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound

Bounded Tamper Resilience

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Faust, Sebastian; Mukherjee, Pratyay

2013-01-01

Related key attacks (RKAs) are powerful cryptanalytic attacks where an adversary can change the secret key and observe the effect of such changes at the output. The state of the art in RKA security protects against an a-priori unbounded number of certain algebraic induced key relations, e.......g., affine functions or polynomials of bounded degree. In this work, we show that it is possible to go beyond the algebraic barrier and achieve security against arbitrary key relations, by restricting the number of tampering queries the adversary is allowed to ask for. The latter restriction is necessary......-protocols (including the Okamoto scheme, for instance) are secure even if the adversary can arbitrarily tamper with the prover’s state a bounded number of times and obtain some bounded amount of leakage. Interestingly, for the Okamoto scheme we can allow also independent tampering with the public parameters. We show...

P2-16: Dual-Bound Model and the Role of Time Bound in Perceptual Decision Making

Directory of Open Access Journals (Sweden)

Daeseob Lim

2012-10-01

Full Text Available The diffusion model (DM encapsulates the dynamics of perceptual decision within a ‘diffusion field’ that is defined by a basis with sensory-evidence (SE and time vectors. At the core of the DM, it assumes that a decision is not made until an evidence particle drifts in the diffusion field and eventually hits one of the two pre-fixed bounds defined in the SE axis. This assumption dictates when and which choice is made by referring to when and which bound will be hit by the evidence particle. What if urgency pressures the decision system to make a choice even when the evidence particle has yet hit the SE bound? Previous modeling attempts at coping with time pressure, despite differences in detail, all manipulated the coordinate of SE bounds. Here, we offer a novel solution by adopting another bound on the time axis. This ‘dual-bound’ model (DBM posits that decisions can also be made when the evidence particle hits a time bound, which is determined on a trial-by-trial basis by a ‘perceived time interval’ – how long the system can stay in the ‘diffusion’ field. The classic single-bound model (SBM exhibited systematic errors in predicting both the reaction time distributions and the time-varying bias in choice. Those errors were not corrected by previously proposed variants of the SBM until the time bound was introduced. The validity of the DBM was further supported by the strong across-individual correlation between observed precision of interval timing and the predicted trial-by-trial variability of the time bound.

Reducing mitochondrial bound hexokinase II mediates transition from non-injurious into injurious ischemia/reperfusion of the intact heart

NARCIS (Netherlands)

R. Nederlof (Rianne); Gürel-Gurevin, E. (Ebru); O. Eerbeek (Otto); C. Xie (Chaoqin); Deijs, G.S.; Konkel, M. (Moritz); Hu, J. (Jun); N.C. Weber (Nina); C. Schumacher (Cees); A. Baartscheer (Antonius); E.G. Mik (Egbert); M.W. Hollmann (Markus); F.G. Akar (Fadi); C.J. Zuurbier (Coert J.)

2016-01-01

textabstractIschemia/reperfusion (I/R) of the heart becomes injurious when duration of the ischemic insult exceeds a certain threshold (approximately ≥20 min). Mitochondrial bound hexokinase II (mtHKII) protects against I/R injury, with the amount of mtHKII correlating with injury. Here, we examine

Bounds on the distribution of the number of gaps when circles and lines are covered by fragments: Theory and practical application to genomic and metagenomic projects

Directory of Open Access Journals (Sweden)

Marchesi Julian R

2007-03-01

Full Text Available Abstract Background The question of how a circle or line segment becomes covered when random arcs are marked off has arisen repeatedly in bioinformatics. The number of uncovered gaps is of particular interest. Approximate distributions for the number of gaps have been given in the literature, one motivation being ease of computation. Error bounds for these approximate distributions have not been given. Results We give bounds on the probability distribution of the number of gaps when a circle is covered by fragments of fixed size. The absolute error in the approximation is typically on the order of 0.1% at 10× coverage depth. The method can be applied to coverage problems on the interval, including edge effects, and applications are given to metagenomic libraries and shotgun sequencing.

Greedy algorithms for construction of approximate tests for decision tables with many-valued decisions

KAUST Repository

Azad, Mohammad

2012-12-14

The paper is devoted to the study of a greedy algorithm for construction of approximate tests (super-reducts) This algorithm is applicable to decision tables with many-valued decisions where each row is labeled with a set of decisions For a given row, we should find a decision from the set attached to this row We consider bounds on the precision of this algorithm relative to the cardinality of tests.

Intensity-based hierarchical elastic registration using approximating splines.

Science.gov (United States)

Serifovic-Trbalic, Amira; Demirovic, Damir; Cattin, Philippe C

2014-01-01

We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces. The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model. The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method. The proposed hierarchical elastic image registration approach incorporates the GEBS

Isotropic LQC and LQC-inspired models with a massless scalar field as generalised Brans-Dicke theories

Science.gov (United States)

Rama, S. Kalyana

2018-06-01

We explore whether generalised Brans-Dicke theories, which have a scalar field Φ and a function ω (Φ ), can be the effective actions leading to the effective equations of motion of the LQC and the LQC-inspired models, which have a massless scalar field σ and a function f( m). We find that this is possible for isotropic cosmology. We relate the pairs (σ , f) and (Φ , ω ) and, using examples, illustrate these relations. We find that near the bounce of the LQC evolutions for which f(m) = sin m, the corresponding field Φ → 0 and the function ω (Φ ) ∝ Φ ^2. We also find that the class of generalised Brans-Dicke theories, which we had found earlier to lead to non singular isotropic evolutions, may be written as an LQC-inspired model. The relations found here in the isotropic cases do not apply to the anisotropic cases, which perhaps require more general effective actions.

Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry

Science.gov (United States)

Gérard, Christian; Oulghazi, Omar; Wrochna, Michał

2017-06-01

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.

AdS{sub 3}/CFT{sub 2}, finite-gap equations and massless modes

Energy Technology Data Exchange (ETDEWEB)

Lloyd, Thomas; Stefański, Bogdan Jr. [Centre for Mathematical Science, City University London,Northampton Square, London EC1V 0HB (United Kingdom)

2014-04-29

It is known that string theory on AdS{sub 3}×M{sub 7} backgrounds, where M{sub 7}=S{sup 3}×S{sup 3}×S{sup 1} or S{sup 3}×T{sup 4}, is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finite-gap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finite-gap equations on these AdS{sub 3}×M{sub 7} backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we re-examine the derivation of the AdS{sub 3}×M{sub 7} finite-gap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finite-gap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS{sub 3}×M{sub 7}.

Bounding the electrostatic free energies associated with linear continuum models of molecular solvation.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G; Anitescu, Mihai

2009-03-14

The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.

Bounding the electrostatic free energies associated with linear continuum models of molecular solvation.

Energy Technology Data Exchange (ETDEWEB)

Bardhan, J. P.; Knepley, M. G.; Anitescu, M. (Biosciences Division); ( MCS); (Rush Univ.)

2009-03-01

The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.

Production of massless bottom jets in p anti p and pp collisions at next-to-leading order of QCD

Energy Technology Data Exchange (ETDEWEB)

Bierenbaum, Isabella [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Kramer, Gustav [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2016-03-15

We present predictions for the inclusive production of bottom jets in proton-antiproton collisions at 1.96 TeV and proton-proton collisions at 7 TeV. The bottom quark is considered massless. In this scheme, we find that at small transverse momentum (p{sub T}) the ratio of the next-to-leading order to the leading-order cross section (K factor) is smaller than one. It increases with increasing p{sub T} and approaches one at larger p{sub T} at a value depending essentially on the choice of the renormalization scale. Adding non-perturbative corrections obtained from PYTHIA Monte Carlo calculations leads to reasonable agreement with experimental b-jet cross sections obtained by the CDF and the CMS collaborations.

Conformal covariance, modular structure, and duality for local algebras in free massless quantum field theories

International Nuclear Information System (INIS)

Hislop, P.D.

1988-01-01

The Tomita modular operators and the duality property for the local von Neumann algebras in quantum field models describing free massless particles with arbitrary helicity are studied. It is proved that the representation of the Poincare group in each model extends to a unitary representation of SU(2, 2), a covering group of the conformal group. An irreducible set of ''standard'' linear fields is shown to be covariant with respect to this representation. The von Neumann algebras associated with wedge, double-cone, and lightcone regions generated by these fields are proved to be unitarily equivalent. The modular operators for these algebras are obtained in explicit form using the conformal covariance and the results of Bisognano and Wichmann on the modular structure of the wedge algebras. The modular automorphism groups are implemented by one-parameter groups of conformal transformations. The modular conjugation operators are used to prove the duality property for the double-cone algebras and the timelike duality property for the lightcone algebras. copyright 1988 Academic Press, Inc

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

Science.gov (United States)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

Bounds on long-lived charged massive particles from Big Bang nucleosynthesis

Energy Technology Data Exchange (ETDEWEB)

Jedamzik, Karsten, E-mail: jedamzik@lpta.univ-montp2.fr [Laboratoire de Physique Mathémathique et Théorique, CNRS, Université de Montpellier II, F-34095 Montpellier Cedex 5 (France)

2008-03-01

The Big Bang nucleosynthesis (BBN) process in the presence of charged massive particles (CHAMPs) is studied in detail. All currently known effects due to the existence of bound states between CHAMPs and nuclei, including possible late-time destruction of {sup 6}Li and {sup 7}Li, are included. The study sets conservative bounds on CHAMP abundances in the decay time range 3×10{sup 2} s∼<τ{sub x}∼<10{sup 12} s. It is stressed that the production of {sup 6}Li at early times T∼10 keV is overestimated by a factor ∼10 when the approximation of the Saha equation for the {sup 4}He bound state fraction is utilized. To obtain conservative limits on the abundance of CHAMPs, a Monte Carlo analysis with ∼3 × 10{sup 6} independent BBN runs, varying the reaction rates of 19 different reactions, is performed. The analysis yields the surprising result that, except for small areas in the particle parameter space, conservative constraints on the abundance of decaying charged particles are currently very close to those of neutral particles. It is shown that, in the case that the rates of a number of heretofore unconsidered reactions may be determined reliably in the future, it is conceivable that the limit on CHAMPs in the early Universe could be tightened by orders of magnitude.

Bounds on long-lived charged massive particles from Big Bang nucleosynthesis

Science.gov (United States)

Jedamzik, Karsten

2008-03-01

The Big Bang nucleosynthesis (BBN) process in the presence of charged massive particles (CHAMPs) is studied in detail. All currently known effects due to the existence of bound states between CHAMPs and nuclei, including possible late-time destruction of 6Li and 7Li, are included. The study sets conservative bounds on CHAMP abundances in the decay time range 3\\times 10^2~\\mathrm {s}\\lesssim \\tau_x\\lesssim 10^{12}~\\mathrm {s} . It is stressed that the production of 6Li at early times T~10 keV is overestimated by a factor ~10 when the approximation of the Saha equation for the 4He bound state fraction is utilized. To obtain conservative limits on the abundance of CHAMPs, a Monte Carlo analysis with ~3 × 106 independent BBN runs, varying the reaction rates of 19 different reactions, is performed. The analysis yields the surprising result that, except for small areas in the particle parameter space, conservative constraints on the abundance of decaying charged particles are currently very close to those of neutral particles. It is shown that, in the case that the rates of a number of heretofore unconsidered reactions may be determined reliably in the future, it is conceivable that the limit on CHAMPs in the early Universe could be tightened by orders of magnitude.

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

Energy Technology Data Exchange (ETDEWEB)

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn [School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Lin, Lin, E-mail: linlin@math.berkeley.edu [Department of Mathematics, University of California, Berkeley, CA 94720 (United States); Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Vigil-Fowler, Derek, E-mail: vigil@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Lischner, Johannes, E-mail: jlischner597@gmail.com [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kemper, Alexander F., E-mail: afkemper@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sharifzadeh, Sahar, E-mail: ssharifz@bu.edu [Department of Electrical and Computer Engineering and Division of Materials Science and Engineering, Boston University, Boston, MA 02215 (United States); Jornada, Felipe H. da, E-mail: jornada@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Deslippe, Jack, E-mail: jdeslippe@lbl.gov [NERSC, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Yang, Chao, E-mail: cyang@lbl.gov [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); and others

2015-04-01

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

A numerical analysis of the Born approximation for image formation modeling of differential interference contrast microscopy for human embryos

Science.gov (United States)

Trattner, Sigal; Feigin, Micha; Greenspan, Hayit; Sochen, Nir

2008-03-01

The differential interference contrast (DIC) microscope is commonly used for the visualization of live biological specimens. It enables the view of the transparent specimens while preserving their viability, being a non-invasive modality. Fertility clinics often use the DIC microscope for evaluation of human embryos quality. Towards quantification and reconstruction of the visualized specimens, an image formation model for DIC imaging is sought and the interaction of light waves with biological matter is examined. In many image formation models the light-matter interaction is expressed via the first Born approximation. The validity region of this approximation is defined in a theoretical bound which limits its use to very small specimens with low dielectric contrast. In this work the Born approximation is investigated via the Helmholtz equation, which describes the interaction between the specimen and light. A solution on the lens field is derived using the Gaussian Legendre quadrature formulation. This numerical scheme is considered both accurate and efficient and has shortened significantly the computation time as compared to integration methods that required a great amount of sampling for satisfying the Whittaker - Shannon sampling theorem. By comparing the numerical results with the theoretical values it is shown that the theoretical bound is not directly relevant to microscopic imaging and is far too limiting. The numerical exhaustive experiments show that the Born approximation is inappropriate for modeling the visualization of thick human embryos.

Instanton bound states in ABJM theory

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

2013-06-15

The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.

A minimal approach to the scattering of physical massless bosons

Science.gov (United States)

Boels, Rutger H.; Luo, Hui

2018-05-01

Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A number of proof-of-concept examples are presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. Dimensional regularisation is employed throughout; different regularisation schemes are worked out explicitly. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, in the introduced approach iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control colour

The approximation of flows

International Nuclear Information System (INIS)

Robinson, D.W.

1975-11-01

Let U,V be two strongly continuous one-parameter groups of bounded operators on a Banach space X with corresponding infinitesimal operators S, T. It is proved that: //U(t)-V(t)//=0(t), t→0, if, and only if, U=V; //U(t)-V(t)//=0 (t.exp.α), t→0, with 0 -1 where OMEGA, P, are bounded operators on X such that //U(t)OMEGA-OMEGA.U(t)//=0(t.exp.α), //U(t)P-PU(t)//=0(t.exp.α); t→0; //U(t)-V(t)//=0(t) if, and only if, S*-T* has a bounded extension to X*. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras [fr