Three-point Amplitudes Research Articles

Fourier spectra of three-dimensional data

view Abstract Citations (78) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fourier Spectra of Three-dimensional Data Baumgart, David J. ; Fry, J. N. Abstract We evaluate the power spectrum, bispectrum, and tentatively the trispectrum, i.e., the two-, three-, and four-point galaxy correlation functions in Fourier transform space, for data from the CfA catalog and from the Perseus-Pisces redshift compilation of Giovanelli & Haynes. We work in the transform domain to avoid many systematic problems that afflict direct evaluations of correlation functions; this enables us to extend our knowledge of galaxy clustering to scales of order 100h^-1^ Mpc. At these large scales, the observed power spectrum ought to reflect directly the initial conditions. Our observed power spectrum agrees well with cold dark matter. The best fit gives {OMEGA}h = 0.34 +/- 0.10, while the inferred amplitude of scale-invariant horizon fluctuations is ɛ~(2-4) x 10^-5^. The observed bispectrum obeys the so-called hierarchical pattern, with a reduced threepoint amplitude that is consistent with gravitational instability in perturbation theory starting from Gaussian initial conditions. The trispectrum is only marginally detected, but is again consistent with the hierarchical pattern; the reduced four-point amplitude is determined only to be of order unity. These results constitute perhaps the first direct observational suggestion that gravitational instability in the perturbative regime indeed operates on large scales. Publication: The Astrophysical Journal Pub Date: July 1991 DOI: 10.1086/170166 Bibcode: 1991ApJ...375...25B Keywords: Fourier Transformation; Galactic Clusters; Galactic Structure; Power Spectra; Three Dimensional Models; Astronomical Catalogs; Computational Astrophysics; Numerical Analysis; Perturbation Theory; Astrophysics; GALAXIES: CLUSTERING; NUMERICAL METHODS full text sources ADS |

Electro-optic AlGaAs spatial light deflector/modulator based on a grating phased array

A novel beam steering device using gratings integrated on rib waveguides as input and output couplers is proposed. Phasing is achieved electro-optically by applying an electric field on an indium-tin-oxide/AlGaAs Schottky junction. A two elements device is first used to characterize the phase modulation characteristics of the structure. A 43 elements device with sawtooth electrodes is then presented, that permits spatial three-point digital beam steering or amplitude modulation. The outcoupled beams have an angular width of 1.8 mrad full width at half maximum. The switched beam angular separation is 9 mrad, the switching voltage is −21 V.

AMPLITUDES IN THE N=2 STRING

We study the properties of amplitudes in the closed string theory based on the N=2 worldsheet supergravity. The one-loop correction to the three-point amplitude is computed and compared to the effective field theory result. We discuss the peculiar kinematics arising from the (2, 2) signature of the space-time and its role in the factorization properties of the amplitudes.

String Interactions on Non-Abelian Orbifold

The systematic prescription for the construction of the tree-level multi-string amplitude on general non-Abelian orbifold is given. The method is applied to some typical examples with the special interest in the three-point amplitudes on the Sg-orbifold. The general formula for the N-point amplitude with two twist points is also given.

Effective Lagrangians for the string model of Bluhm, Dolan, and Goddard. II. The fermionic sector.

We have studied all the massless three-point and massless four-point tree amplitudes of the Bluhm-Dolan-Goddard string model, now including the fermions. In our study, we have decomposed the ten-dimensional spinors into four families of four-dimensional Majorana spinors. With these four-dimensional spinors, we are able to write the effective Lagrangians, inferred from the low-energy limit of the string amplitudes, in terms of four-dimensional fermionic fields. In this four-dimensional form, the Lagrangians contain terms that will describe conventional supergravity within the same family. There will also be interfamily interactions mediated by the neutral vectors and gauge scalars.

Chiral bosonization and vanishing of the three-point amplitude at two loops in the heterotic string.

Using chiral bosonization we explicitly show that the fermion-fermion-boson amplitude in the heterotic string at two loops vanishes through the Riemann theta identity. Chiral bosonization is applied to the computation of the correlation functions for the spin operators of the superconformal ghost system.

COMMENT ON THE NON-RENORMALIZATION THEOREM IN FOUR-DIMENSIONAL STRING THEORY AND VANISHING β-FUNCTION FOR NEWTON’S CONSTANT

Three-point one-loop amplitude for the graviton is considered in the string theory compactified on orbifolds with N=1 supersymmetry. We show that the amplitude leads to the vanishing correction to the Newton’s constant.

One-loop amplitudes on orbifolds and the renormalization of coupling constants

We consider three-point one-loop amplitudes for strings propagating on orbifolds that preserve a supersymmetry. For three external gauge bosons, we compute the explicit wave-function renormalization of the external legs and show that it leads to the correct value for the Yang-Mills β-function. For two gauge bosons and a graviton, we show that there is no renormalization of the coupling, but if the graviton is replaced with an antisymmetric tensor, then the coupling is renormalized.

Comment on the non-renormalization theorem in the four-dimensional superstrings

We discuss the non-renormalization theorem in the context of the four-dimensional superstrings. We explicitly demonstrate that the graviton three-point one-loop amplitude does not vanish in contrast to the ten-dimensional superstring theories.

The heterotic string and supersymmetric counterparts of the Lorentz Chern-Simons terms

The heterotic string three-point amplitude, which involves two fermionic and one bosonic state, determines some of the terms that must be added to the action of the N=1 supergravity coupled to N=1 supersymmetric Yang-Mills in ten dimensions to preserve supersymmetry, if the Lorentz Chern-Simons term is included in the definition of the field strength H μνϱ for the cancellation of anomalies. Our calculation reveals an interesting structure, which suggests that the relevant H-Bianchi for the analysis of possible heterotic string compactifications involves a spin connection possibly with torsion.

Thermodynamics and galaxy clustering - Analysis of the center for astrophysics redshift catalog

view Abstract Citations (34) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Thermodynamics and galaxy clustering: analysis of the Center for Astrophysics redshift catalog. Hamilton, A. J. S. ; Saslaw, W. C. ; Thuan, T. X. Abstract In a recent paper Saslaw and Hamilton developed distribution functions for homogeneous gravitational clustering and found substantial agreement with N-body simulations of galaxy clustering from random initial conditions. The present paper compares these distributions to the observed distributions from the Center for Astrophysics redshift galaxy catalog, using formal statistical tests. In order to obtain the best possible signal-to-noise, a new method is used to stack the data from many volume-limited subsamples. It is found that the distributions are consistent with the observations at about the same level that the observations are consistent among themselves, as judged from one- and two-sample chi-squared tests of significance. The theoretical distributions have three-point correlation amplitudes between 0.75 and 1 and multiplicity functions with the same form as the multiplicity function proposed by Press and Schechter for a galaxy distribution evolved from random initial conditions; both these results are known to be consistent with observations. Publication: The Astrophysical Journal Pub Date: October 1985 DOI: 10.1086/163501 Bibcode: 1985ApJ...297...37H Keywords: Astronomical Catalogs; Distribution Functions; Galactic Clusters; Red Shift; Statistical Tests; Thermodynamics; Cosmology; Random Processes; Signal To Noise Ratios; Astrophysics; Cosmology:Galaxy Clustering; Galaxies:Redshifts; Galaxy Clustering:Cosmology; Redshifts:Galaxies full text sources ADS |

The Galaxy correlation hierarchy in perturbation theory

view Abstract Citations (489) References (22) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Galaxy correlation hierarchy in perturbation theory Fry, J. N. Abstract The evolution of cosmological density correlation functions is calculated to lowest nonvanishing order in perturbation theory for an initially random Gaussian distribution. The three-point function so obtained scales with size as in the continuous-hierarchy model, but there is a residual nontrivial dependence on shape of the reduced three-point amplitude Q. The average value Q = 34/21 - (1/6) gamma is consistent with observations in the nonperturbative regime. The four-point function is also hierarchical in form, with amplitudes Ra = (34/21)2 and Rb = 682/189. The perturbation expansion in fact gives kappa(N) proportional to xi to the (N-1) for the reduced correlation function kappa(N) to all orders N. A graphical technique enumerates the terms which appear in kappa(N). Publication: The Astrophysical Journal Pub Date: April 1984 DOI: 10.1086/161913 Bibcode: 1984ApJ...279..499F Keywords: Big Bang Cosmology; Galactic Clusters; Perturbation Theory; Universe; Astronomical Models; Correlation; Fourier Transformation; Functions (Mathematics); Hierarchies; Astrophysics full text sources ADS |

Galaxy N-point correlation functions - Theoretical amplitudes for arbitrary N

Scaling arguments have suggested the hierarchical form of galaxy N-point correlation functions, kappa/sub N/ = Q/sub N/xi/sup N/-1, where xi is the two-point function, but such arguments are inherently unable to predict the amplitudes Q/sub N/. Assuming this form, substituting in the BBGKY hierarchy, and using graph theory combinatories, I find amplitudes Q/sub N/ = (4Q/N)/sup N/-2N/(2N-2), where Q is the reduced three-point amplitude. As an application, I compute the probability of large void regions in the hierarchical picture.

Structure of hadron in Migdal's regularization scheme for QCD

Migdal's approach to the spectrum of QCD is generalized to three-point (hadron) amplitudes. This procedure is shown to be unique once the two-point functions are known. In particular, meson form factors and structure functions are discussed including hard gluon and Regge contributions. Quark mass effects turn out to be very important.

A dynamical model of baryons with the spinor-scalar Bethe-Salpeter equation

The first part of the paper contains a systematic study of the spinor-scalar Bethe-Salpeter equation with a scalar ladder-like interaction. By expansion and truncation procedures a finite system of linear homogeneous equations is obtained which represent the Bethe-Salpeter equation in the space of convenient basis functions. In the second part a relativistic parton model of baryons is suggested. The three-point Bethe-Salpeter amplitude of the bound state baryon is approximated by a decomposition which involves the solutions of a generalized spinor-scalar Bethe-Salpeter equation. These solutions might be interpreted as the single-parton amplitudes. It is assumed that the long-range effective interaction has a Coulomb-type asymptotic behaviour. A linear leading Regge trajectory is achieved by assuming that the effective mass of partons is a particular function of the c.m. energy of the baryon.

Infinite Multiplets and Crossing Symmetry. I. Three-Point Amplitudes

This paper investigates what remains of crossing symmetry in theories that are conventional local field theories in all but one respect: that infinite irreducible representations of the homogeneous Lorentz group are used. Only vertex functions are studied here; results for scattering amplitudes will be reported in a sequel. It is found that: (i) Form factors for scattering ($t<0$) and form factors for annihilation ($t>4{m}^{2}$) are strongly related to each other by the requirement that the interaction Lagrangian density be local, but they are not connected by analytic continuation. (ii) In the case of half-integral-spin fields, the empirical fact that the parities of particles and antiparticles are opposite makes it necessary to use a pair of conjugate irreducible representations, rather than a single unitary irreducible representation. An analog of the Dirac equation allows one to avoid parity doubling and to ensure a proper physical interpretation, provided that quantization is carried out with anticommutators.

Nonperturbative solutions in a field theory withSp 6 symmetry

AnSp6-invariant nonlinear spinor equation is introduced and discussed. The covariant Fock equations are considered by using nonperturbative methods based on appropriate decompositions of many-point amplitudes. In the first part of the paper an exactSp6 symmetry is assumed taking into account the possible spontaneous breakdown of theγ5-invariance. In order to avoid the divergence difficulties, some self-consistent boundary conditions are imposed to be satisfied by the two- and three-point amplitudes for vanishing relative co-ordinates. These self-consistent boundary conditions cannot be satisfied in a trivial way due to the well-known singularities of the relativistic interactions. A kind of eigenvalue problem is obtained for the couplings and masses. The results indicate that an acceptable solution of the problem is not excluded. This possibility is connected with the simultaneous occurence of the interactions generated by trion-antitrion pairs characterized by spin zero and one. The coupling generated by pseudoscalar pairs is a derivative one. For pseudoscalar trion-antitrion amplitudes the fulfilment of the self-consistent boundary conditions is discussed in detail in the framework of the nonperturbative methods introduced in this paper. The self-consistent boundary conditions can be satisfied if the bare coupling constantg0(11) characterizing the coupling of trions toSp6 singlet trion-antitrion pairs with spin one is fixed by (g0(11))2=12π2. The coupling of trions toSp6 singlet pseudoscalar pairs has to satisfy a simple self-consistent subsidiary condition. The other couplings of trions vanish. No conflict, with the general framework of relativistic quantum field theory appears; the usual finite cut-off is not introduced. Only the action principle is rejected. In the second part of the paper the possibility of the spontaneous medium-strong breakdown of theSp6-invariance is discussed in detail.