Showing papers on "Antisymmetric relation published in 1985"
TL;DR: In this paper, the effect of Wess-Zumino terms on nonlinear sigma models with torsion on the field manifold has been investigated in two dimensions, showing that the geometrical aspects of such models carry over completely.
298 citations
TL;DR: In this paper, the complete N = 8 d = 5 supergravity action and supersymmetry transformation laws (without four and three-fermion terms) were obtained from the ungauged model by reinterpreting part of the field strenghts of the abelian vector fields as real self-dual second-rank antisymmetric tensors.
199 citations
TL;DR: Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed and another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields is developed.
Abstract: Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.
125 citations
TL;DR: In this paper, the eigenvalues of the quantum hamiltonians with two degrees of freedom were computed numerically and it was shown that each perturbation alone leads to the level statistics of the gaussian orthogonal ensemble.
45 citations
TL;DR: In this paper, a new formalism is proposed for calculating perturbation energy corrections for the case of two interacting molecules at any distance, and the perturbational problem is handled by introducing a biorthogonal (reciprocal) basis set.
41 citations
TL;DR: In this paper, the generator-coordinate method and the microscopic R -matrix formalism are applied to the description of nucleus-nucleus bremsstrahlung with antisymmetric wave functions.
31 citations
01 Jan 1985
20 citations
TL;DR: In this paper, a finite element formulation applicable to the general shell of revolution is presented for the stress and stability analysis of toroidal pressure vessels under hydrostatic pressure considering the follower force effect of the external pressure, linear bifurcation buckling loads and corresponding mode shapes.
17 citations
TL;DR: This paper presents a new method based on the concept of a ``mirror potential,'' which is a many-body potential that forces the Monte Carlo iteration to have a stable antisymmetric component, and offers an approximation analogous to fixed node for treating systems with noncentral forces.
Abstract: The exact treatment of fermion systems by Monte Carlo methods has proved to be difficult. We present a new method based on the concept of a ``mirror potential,'' which is a many-body potential that forces the Monte Carlo iteration to have a stable antisymmetric component. The potential may be determined from the wave function and, within the framework of Green's function Monte Carlo, from the random walk whose density converges to the wave function. In certain limits, the method reduces to the fixed node approximation and to transient estimation, so that it subsumes both of them. As a further consequence it offers an approximation analogous to fixed node for treating systems with noncentral forces. The method may prove to be a general one for treating random walkers with nonpositive or complex weights. In support of that we exhibit a successful calculation of a one-dimensional excited state. In this paper we explore the alternative in which the mirror potential is obtained from trial wave functions. This yields an approximation scheme that proves to be accurate in the experiments described here. We present results for a model problem in which four neutrons interact by a spin-independent potential, and compare the results with those of the fixed node method, and the method of transient estimation.
17 citations
TL;DR: A review of methods for solving the radiation transport equation in terms of the symmetric and antisymmetric averages first introduced by Feautrier can be found in this paper, where both formulation and algorithms are discussed briefly and basic references are provided in order to provide easy access to workers in other fields where these methods may prove applicable.
14 citations
TL;DR: In this paper, a spin-tensor decomposition of the matrix elements is made and comparisons are presented for the separated central, tensor, spin-orbit and antisymmetric spinorbit components.
Abstract: New empirical two-body matrix elements derived from the spectra of 1s-0d shell nuclei are compared with previous empirical results and with the G-matrix elements obtained from the Reid soft-core and Paris potentials. A spin-tensor decomposition of the matrix elements is made and comparisons are presented for the separated central, tensor, spin-orbit and antisymmetric spin-orbit components.
TL;DR: In this paper, a truncated model was proposed to model blocking patterns with a local approach, where stationary coherent structures were found as asymptotic solutions of the inviscid, quasi-geostrophic potential vorticity equation with a mean zonal wind with vertical and horizontal shear.
Abstract: Many recent studies have been devoted to atmospheric Patterns that persist beyond the synoptic time scale, such as those known as blocking events. In the present paper we explore the possibility that blocking patterns can be modeled with a local approach. We propose a truncated model that is a time-dependent, highly nonlinear extension of our earlier analytical theory. In this theory, stationary coherent structures were found as asymptotic solutions of the inviscid, quasi-geostrophic potential vorticity equation with a mean zonal wind with vertical and horizontal shear, in the limit of weak dispersion and weak nonlinearity. The truncated model is obtained by projecting the potential vorticity equation onto the orthonormal basis defined by the lowest order problem of the asymptotic theory and then suitably truncating the number of modes. The time-evolution of the model is investigated numerically with different truncations. The steady solutions were antisymmetric dipoles, with the anticyclone nort...
TL;DR: A sequence of three-letter words was constructed for the antisymmetric map Xn+1=F(Xn,A)=A*Xn+(1-A)*Xn as discussed by the authors, which contains all the information about the occurrence of periodic windows on the parameter axis.
Abstract: A sequence of three-letter words was constructed for the antisymmetric map Xn+1=F(Xn,A)=A*Xn+(1-A)*Xn, which contains all the information about the occurrence of periodic windows on the parameter axis.
TL;DR: In this paper, the authors consider a Lagrangian density with nine terms linear or quadratic in the curvature and the torsion tensors and derive the conditions which the parameters have to satisfy in order to avoid zero-mass ghosts.
Abstract: In the framework of a Poincare gange theory, we consider a Lagrangian density containing nine terms linear or quadratic in the curvature and the torsion tensors. We consider the zero-mass normal modes of the linearized theory and we derive the conditions which the parameters have to satisfy in order to avoid zero-mass ghosts. We consider in detail the additional gauge transformations and the corresponding constraints on the sources which appear for some special values of the parameters. We conclude that a long-range propagation of the totally antisymmetric part of the torsion is not compatible with the absence of ghosts and of unphysical constraints on the sources.
TL;DR: In this article, the authors derived N-representability conditions for a two-particle density operator implied by positive-semidefiniteness of the projection operator PN+1(ϕ1 Λ ΨN) and analyzed the facial structure of the convex set 2N exposed by elements of 2N(g, q).
Abstract: N-representability conditions for a two-particle density operator implied by positive-semidefiniteness of the projection operator PN+1(ϕ1 Λ ΨN) are derived and discussed. The operator PN+1(ϕ1 Λ ΨN) projects onto an (N + 1)-particle antisymmetric function ϕ1 Λ ΨN, the Grassmann product of a one-particle factor ϕ1 and an N-particle factor ΨN. The polar subcone 2N(g, q) to the set of N-representable two-particle density operators 2N which corresponds to these conditions is found. It is shown that its extreme rays belong to two orbits for the action of the unitary group of transformations in one-particle Hilbert space. The facial structure of the convex set 2N exposed by elements of 2N(g, q) is analyzed. An example of the operator that changes the structure of its bottom eigenspace when the number of fermions N surpasses a certain value is noted. A new approach to the diagonal conditions for N-representability is found. It consists of the decomposition of the N-particle antisymmetric identity operator onto the mutually orthogonal projection operators.
TL;DR: In this paper, a half-space containing a surface-breaking crack of uniform depth is subjected to three-dimensional dynamic loading, and the elastodynamic stress analysis problem is decomposed into two problems, which are symmetric and antisymmetric, respectively, relative to the plane of the crack.
Abstract: A half-space containing a surface-breaking crack of uniform depth is subjected to three-dimensional dynamic loading. The elastodynamic stress-analysis problem has been decomposed into two problems, which are symmetric and antisymmetric, respectively, relative to the plane of the crack. The formulation of each problem has been reduced to a system of singular integral equations of the first kind. The symmetric problem is governed by a single integral equation for the opening-mode dislocation density. A pair of coupled integral equations for the two sliding-mode dislocation densities govern the antisymmetric problem. The systems of integral equations are solved numerically. The stress-intensity factors are obtained directly from the dislocation densities. The formulation is valid for arbitrary 3-D loading of the half-space. As an example, an applied stress field corresponding to an incident Rayleigh surface wave has been considered. The dependence of the stress-intensity factors on the frequency, and on the angle of incidence, is displayed in a set of figures.
TL;DR: In this paper, the stability analysis of linear triatomic molecules having local Morse bonding potentials was studied using the Floquet theory. But the analysis was restricted to the case where the frequency of the antisymmetric normal mode frequency is fixed.
Abstract: Floquet theory is applied to the stability analysis of linear triatomic molecules having local Morse bonding potentials. We identify conditions for the existence of a symmetric mode and analyze its stability as a function of the energy and symmetric to antisymmetric normal mode frequency ratio. In the stable region we apply a special phase normalization to the Floquet eigenvalues that allows us to identify factors in the Floquet index with a red‐shifted generalized antisymmetric mode frequency. Instabilities set in when the ratio of this frequency to the symmetric mode frequency is integer or half‐integer. Analytic forms for Poincare surfaces of section valid for the linearized theory are derived and compared with actual trajectory intersections for both stable and unstable cases. In the stable (quasiperiodic) cases, surfaces corresponding to different sections are ellipses with varying eccentricity but constant area. Hyperbolas are obtained in unstable cases.
TL;DR: In this paper, specific formulas for the single-group effective diffusion coefficient used in the SHM equations for plane, square, hexahedral, and cylindrical cells in terms of the angular moments of the antisymmetric neutron distribution function at the cell boundary were obtained.
Abstract: Specific formulas are obtained for the single-group effective diffusion coefficient used in the SHM equations for plane, square, hexahedral, and cylindrical cells in terms of the angular moments of the antisymmetric neutron distribution function at the cell boundary. The limits of validity of neglecting the second angular moments are tested. It is shown that, for dense grids, this leads to larger errors, which explains the previously incomprehensible results.
01 Jan 1985
TL;DR: In this paper, the basic results of density functional theory are reviewed, including the lemma of Hohenberg and Kohn establishing the density n(r) as a sufficient variable for a description of a non-degenerate or degenerate ground state; recent reformulations by Levy and Lieb; the selfconsistent Kohn-Sham equations and the most recent improved approximations for the exchange-correlation functional.
Abstract: We review first the basic results of density functional theory: the lemma of Hohenberg and Kohn establishing the density n(r) as a sufficient variable for a description of a non-degenerate or degenerate ground state; the energy variational principle, including recent reformulations by Levy and Lieb; the self-consistent Kohn-Sham equations and the most recent improved approximations for the exchange-correlation functional. This is followed by a number of observations: the issue of v-representability is discussed, including, depending on the context, its significance and non-significance in the light of recent work by Levy, Lieb, and Kohn; a discussion is presented of two different approaches to the basic functionals F[n(r)] and Exc[n(r)] -- by means of many-body tech-niques or by using the definition of F[n(r)] as a minimum over a constrained set of antisymmetric functions; other interesting recent developments of density functionals are briefly mentioned; some remarks are offered concerning a proposed concept of generalized local approximations; and finally a few other promising directions for future research are listed.
TL;DR: In this paper, a method of calculating the antisymmetric neutron distributions in the single group approximation is proposed for a multizone cylindrical cell and the neutron distribution in zone h of the cell is described by the single-group neutron-transfer equation in the transport approximation.
Abstract: A method of calculating the antisymmetric neutron distributions in the single group approximation is proposed. A multizone cylindrical cell is considered and the neutron distribution in zone h of the cell is described by the single-group neutron-transfer equation in the transport approximation. The authors discuss using the surfacpseudosource method to calculate the distributions and the matrixfactorizing method is described. The ORAR-Ts program is examined which calculates the single-group antisymmetric neutron distributions in a cylindrical reactor cell with a specified current at the external cell boundary in the G/sub 1/ and G/sub 3/ approximations of the SPM. Calculation results are presented.
TL;DR: In this article, the authors derived exact expressions and asymptotic forms for the density-density correlation function, using periodic boundary conditions, and for density (magnetization) profile, using antisymmetric boundary conditions.
Abstract: A one-dimensional lattice gas (Ising model) of lengthL and with nearest-neighbor couplingJ is considered in a canonical ensemble with fixed number of particlesN=L/2. Exact expressions and asymptotic forms for largeL are derived for the density-density correlation function, using periodic boundary conditions, and for the density (magnetization) profile, using antisymmetric boundary conditions. The density-density correlation function,g, assumes for temperaturesT> T, withT = 2J(κBlnL)−1 and forL large, the formg(x) =ggc(x) +BL−1 +a(x)L−1 +O(L−2) wherex is a distance between considered lattice sites,B is known from earlier work of Lebowitz and Percus,(1b) anda(x) decays exponentially forx → ∞. For T⩽T′, the correlation function and the density profile behave differently, the latter exhibiting a step in the middle of the interface.
TL;DR: In this paper, the authors investigated the sensitivity of the proton magnetic form factor to the choice of the wave function and found that the actual size of the form factor can only be fitted at the expense of the shape at lower Q2.
Abstract: The author investigates the sensitivity of the proton magnetic form factor to the choice of the wavefunction. He employs next-to-leading terms in the proton distribution amplitude in an attempt to modify the zero asymptotic result and fit the form of the experimental curve. He finds that the actual size of the form factor can only be fitted at the expense of the shape at lower Q2. The best compromise includes an antisymmetric component and is within an order of magnitude of the data.
TL;DR: The 124 completely antisymmetric fijk and 221 completely symmetric dijk (nonzero) structure constants for a simple representation of SU(6) are tabulated in this paper.
Abstract: The 124 completely antisymmetric fijk and 221 completely symmetric dijk (nonzero) structure constants for a simple representation of SU(6) are tabulated. The basis matrices λi used to generate the structure constants are also given.
TL;DR: In this article, an approximate theory for the transverse motion of a two-layered plate is developed, where the two layers are assumed to be elastic, isotropic, homogeneous and welded to each other.
TL;DR: In this article, the authors deduce from the closure of the supersymmetry algebra at the linearized level on the bosons necessary conditions for the consistency of the coupling of a gauge antisymmetric tensor field A μ 1, μn −1 to supergravity in a d -dimensional space-time.
TL;DR: In this paper, the spinor approach was used to show that the conserved total energy-momentum vector in ann-dimensional Lorentzian space is nonspace-like.
Abstract: The spinor approach of Witten and Nester is used to show that in ann-dimensional Lorentzian spaceVn, the conserved total energy-momentum vectorPα is nonspace-like. It is shown thatPα may be expressed in terms of an integral of an antisymmetric tensorEαβ over ann − 2-dimensional subspace at space-like infinity inVn.Eαβ is expressed in terms of a spinor field inVn and its covariant derivatives. This tensor is a generalization of that used in the discussion of five-dimensional Lorentzian spaces.
01 Jan 1985
TL;DR: In this article, transient plasma-physics/electromagnetic codes were used to analyze microwave tube circuits excited by an unmodulated electron beam, and the capability of these programs to perform quantitative stability analysis on microwave tube plus beam was demonstrated.
Abstract: Transient plasma-physics/electromagnetic codes were used to analyze microwave tube circuits excited by an unmodulated electron beam. The objective was to assess the value of Mission Research Corporation's codes "SOS" and "MAGIC" (for 3- and 2-dimensional analysis, respectively) for analysis of oscillation in microwave tubes. For the 2-D case the Q of a cavity due to beam loading was obtained and corroborated by other methods. For the 3-D cases the computed resonance frequencies in a resonated section of coupled-cavity TWT were corroborated by cold-test measurement. Despite the coarse frequency resolution inherent in the relatively short-duration transient analysis performed for a higher-order antisymmetric mode, it was possible to isolate several of the resonances sufficiently to determine the negative Q due to beam loading. Thus the capability of these programs to perform quantitative stability analysis on microwave tube circuits plus beam was demonstrated.
TL;DR: In this paper, the totally symmetric and totally antisymmetric direct couplings of fermions in d−dimensional space are investigated and explicit forms are given for d ≥ 11.
Abstract: The totally symmetric and totally antisymmetric direct couplings of fermions in d‐dimensional space are investigated. Explicit forms are given for d<11. A different way of handling the d‐dimensional Dirac algebra is also described.
15 Apr 1985
01 Sep 1985
TL;DR: In this article, a formalism for the evolution in Q/sub 2/ of multiquark systems as an application of perturbative quantum chromodynamics (QCD) to asymptotic, exclusive nuclear amplitudes is presented.
Abstract: We present a formalism for the evolution in Q/sub 2/ of multiquark systems as an application of perturbative quantum chromodynamics (QCD) to asymptotic, exclusive nuclear amplitudes. To leading terms in log Q/sup 2/ our formalism is equivalent to solving the renormalization group equations for these amplitudes. Completely antisymmetric multiquark color-singlet represntations are constructed and their evolution is investigated from the one-gluon exchange kernel. We argue that the evolution equation, together with a cluster decomposition, demonstrates a transition from the traditional meson and nucleon degrees of freedom of nuclear physics to quark and gluon degrees of freedom with increasing Q/sup 2/, or at small internucleon separation. As an example, we derive an evolution equation for a completely antisymmetric six-quark distribution amplitude and solve the evolution equation for a deuteron S-wave amplitude. The leading anomalous dimension and the corresponding eigensolution are found for the deuteron in order to predict the asymptotic form of the deuteron distribution amplitude (i.e., light-cone wave function at short distances). The fact that the six-quark state is 80 percent hidden color at small transverse separation implies that the deuteron form factor cannot be described at large Q/sup 2/ by meson-nucleon degrees of freedom alone. Furthermore, since the N-Nmore » channel is very suppressed under these conditions, the effective nucleon-nucleon potential is naturally repulsive at short distances. 20 refs.« less