Showing papers on "Symmetry (physics) published in 1981"
TL;DR: In this article, the deconvolution of the convolution square of a symmetrical function with a limited range of definition is presented. And the influence of imperfect realization of the symmetry conditions is discussed.
Abstract: A method for the deconvolution of the convolution square of a symmetrical function with a limited range of definition is presented. The solution function is approximated by a number of equidistant step functions. This allows the analytical computation of the integrals of overlap in one-dimensional (lamellar) symmetry, in two-dimensional (cylindrical) symmetry and in three-dimensional (spherical) symmetry. A special iterative linearized weighted-least-squares technique solves the non-linear convolution square-root problem without any a priori information on the solution. As an application, the electron or scattering length density ρ(r) from the distance distribution function p(r) of small-angle scattering is computed as well as the propagation of the statistical error from the input. The influence of imperfect realization of the symmetry conditions is discussed. Numerical instabilities that appear under certain conditions can easily be removed by a stabilization procedure.
216 citations
TL;DR: In this paper, the spectral function sum rules were used to determine the symmetry breakdown pattern of the electroweak symmetry breakdown for a large class of models, including weak mixing angles and pseudo-Goldstone bosons.
196 citations
TL;DR: In this article, it was shown that in an SU(2) lattice gauge theory, in the approximation where internal quark closed loops are neglected, chiral symmetry is broken.
Abstract: It is shown that in an SU(2) lattice gauge theory, in the approximation where internal quark closed loops are neglected, chiral symmetry is broken. With use of partially conserved axial-vector current f/sub ..pi../, the bare masses of the u and d quarks, and the rho and delta masses are estimated.
193 citations
TL;DR: In this article, it was shown that the zero set of a momentum mapping has a singularity at each point with symmetry, in the sense of a pure gauge with symmetry; the proof uses the Kuranishi theory of deformations.
Abstract: The zero set of a momentum mapping is shown to have a singularity
at each point with symmetry. The zero set is diffeomorphic to the product of a
manifold and the zero set of a homogeneous quadratic function. The proof uses
the Kuranishi theory of deformations. Among the applications, it is shown that
the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a
singularity at any solution with symmetry, in the sense of a pure gauge
symmetry. Similarly, the set of solutions of Einstein's equations has a
singularity at any solution that has spacelike Killing fields, provided the
spacetime has a compact Cauchy surface.
181 citations
TL;DR: In this paper, the interacting boson model is related to the collective and shell models, and even-even nuclei are considered in the context of the AIP (Even-Even Particle Interaction) model.
Abstract: The interacting boson model is related to the collective and shell models. Even-even nuclei are considered. (AIP)
160 citations
129 citations
TL;DR: In this paper, the Faddeev-Popov ghost fields appear as parameters of a gauge transformation in a suitable geometrical structure, a fibre bundle constructed over a 4+2 superspace with a suitable supergroup.
Abstract: We present here the geometry of the superfield formulation of the extended BRS symmetry. The Faddeev-Popov ghost fields appear as parameters of a gauge transformation in a suitable geometrical structureQ(M
S,G
S), a fibre bundle constructed over a 4+2 superspaceM
S with a suitable supergroupG
S as «structure group».
106 citations
TL;DR: In this paper, the average density and two-point correlation function are given in the general case in terms of the corresponding Stieltjes transforms, first used by Pastur for the density.
84 citations
TL;DR: The standard version of Noether's theorem, when applied to the classical Kepler problem, leads to the constants of energy and angular momentum, but does not give the hidden symmetry known as the Runge-Lenz vector as discussed by the authors.
Abstract: The standard version of Noether's theorem, when applied to the classical Kepler problem, leads to the constants of energy and angular momentum, but does not give the 'hidden symmetry' known as the Runge-Lenz vector. Lie's theory of differential equations is used to obtain all three constants of motion. The transformations of solutions under the point transformations to which these constants correspond are studied. The results are generalised to n dimensions.
83 citations
TL;DR: In this article, the spinor symmetries of the interacting boson-fermion model were discussed and closed expressions for energies, electromagnetic (EO, M1, E2) transition rates, static moments and (one and two) nucleon transfer reaction intensities were derived.
TL;DR: In this article, it was shown that, for O 2, in a MC SCF determination of the core ionization potentials employing the full Molecular point group, very few (N -1)-particle configurations are required in order to account for the symmetry breaking in the corresponding Hartree-Fock calculations.
TL;DR: In this paper, the authors extended symmetry methods employed in the ab initio polyatomic program HONDO to the analytic computation of the energy Hessian matrix, which is generated by projecting the symmetric component out of the skeleton Hessian.
Abstract: Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the analytic computation of the energy Hessian matrix. A ’’skeleton’’ Hessian matrix is calculated from the unique blocks of electron repulsion integrals. The true Hessian matrix is generated by projecting the symmetric component out of the skeleton Hessian. The analysis is valid for many wave functions, including closed‐ or open‐shell restricted and unrestricted Hartree–Fock wave functions, multiconfiguration Hartree–Fock wave functions, and configuration interaction wave functions. We also extend the use of translational invariance previously used for energy gradient calculations. To illustrate the method, we compare the computer time required for the two‐electron contribution to the Hessian matrix of eclipsed ethane, using Pople’s 6‐31G basis set and D3h symmetry and various subgroups of D3h. Computational times are roughly inversely proportional to the order of the point group.
TL;DR: For one degree of freedom systems, the answer to this question is affirmative as discussed by the authors, and the construction of a suitable constant of the motion F for given symmetry Y and vice versa.
Abstract: Deals with the following question: given a symmetry vector field Y of a system of second-order ordinary differential equations, and an associated constant of the motion F, is it possible to find a Lagrangian L for the system, such that Y becomes a Noether symmetry with respect to L, and F its implied Noether constant? For one degree of freedom systems the answer to this question is affirmative. In addition, attention is paid to the construction of a suitable constant of the motion F for given symmetry Y and vice versa. Several examples are discussed.
01 Sep 1981
TL;DR: In this paper, the authors show that the degeneracy space for this form is tangent to a manifold of symmetric solutions and symmetry breaking occurs for perturbations in the non-degenerate directions of the quadratic form.
Abstract: The solution set for the (sourceless) Yang-Mills equations on a spacetime with compact Cauchy surface is a smooth manifold (i.e. the equations are linearization stable) except at solutions that are symmetric. At such symmetric solutions, the structure is described by a homogeneous quadratic form. The degeneracy space for this form is tangent to a manifold of symmetric solutions. Symmetry breaking occurs for perturbations in the nondegenerate directions of the quadratic form. The terms ‘symmetry’ and ‘stability’ in the present work are compared to these terms as used elsewhere in the literature.
TL;DR: In this article, the onset of symmetry breaking in the chiral SU(n) × SU (n) linear σ model is investigated and it is shown that the model possesses no stable fixed points in d = 4 − ϵ dimensions.
TL;DR: In this article, the group manifold method is used to derive the χ-space constraints as field equations and a duality relation between the dilaton and axion curvatures that results in a purely geometric second-order action without Maxwell term.
TL;DR: In this paper, the rotational wave functions, which transform according to each of the irreducible representations of the tetrahedral symmetry, are defined and a new interaction potential for the Ar-CH4 system is used.
Abstract: Close‐coupling and coupled states integral, differential, and total cross sections in an argon–methane scattering system are presented for all the irreducible representations of the tetrahedral symmetry. From symmetry considerations the rotational wave functions, which transform according to each of the irreducible representations, are defined. A new interaction potential for the Ar–CH4 system is used. The spherically symmetric part of the potential is due to U. Buck, and was found by fitting a flexible Morse‐spline–Morse‐spline–van der Waals curve to total differential cross section. In the present paper an anisotropic term was added to the potential. Scattering from normal methane consisting of a mixture of all of the symmetries is discussed. Close‐coupling and coupled states cross sections are compared for all the representations. Errors in the coupled states approximation run to 30%. Calculations with a Lennard‐Jones interaction potential show that the magnitude of the percentage error in the coupled states cross sections is potential dependent. Coupled states integral, differential, and total cross sections for normal methane are presented over the energy range from 246 to 582 cm−1 (30–72 meV). The effect of compound state resonances on this system is illustrated.
01 Jan 1981
TL;DR: In this paper, a review of results obtained at the Institute for Mathematics at Fudan University in cooperation with Prof. C.N. Yang at Stony Brook is presented.
TL;DR: In this article, a complete description of all possible sample symmetries can be given in terms of black-white symmetry groups, and the determination of the odd part of the texture function is strongly related to these groups and the various kinds of the inversion centre.
TL;DR: In this paper, the magnetohydrodynamic dynamo problem for an electrically conducting spherical fluid shell with spherically symmetric distributions of gravity and heat sources is solved and the dynamics of motions generated by thermal buoyancy are dominated by the effects of rotation of the fluid shell.
01 Dec 1981
TL;DR: In this paper, a linear feedback law is obtained in closed form for the regulation of the angular momentum of an arbitrary rotating rigid body, without linearizing hypotheses of symmetry, yet optimal for a suitable quadratic energy cost.
Abstract: A linear feedback law is obtained in closed form for the regulation of the angular momentum of an arbitrary rotating rigid body, without linearizing hypotheses of symmetry, yet optimal for a suitable quadratic energy cost. The evolution of the amplitude of the controlled angular momentum is thereby obtained in closed form, whence asymptotic closed-loop stability and exact open-loop terminal rate nulling are derived. Earlier steady-state results are recovered as particular cases.
TL;DR: In this article, the symmetry of the differential system for elastic waves, previously noted for plane geometry, is extended to any linear differential system and, in particular, the elastic-gravitational vibrations in a spherical earth.
Abstract: Summary. The symmetry of the differential system for elastic waves, previously noted for plane geometry, is extended to any linear differential system and, in particular, the elastic-gravitational vibrations in a spherical earth. The result remains valid in a linearly viscoelastic medium. The symmetry allows the inverse of the propagator matrix to be obtained by simply ‘transposing’ the elements of the propagator. With this result, it is shown how the source excitation using a particular integral can be put in a more instructive form, comparable with the result for the excitation of normal modes.
TL;DR: In this article, a geometrical model of the process of radiative transfer for polarized radiation is given by generalizing the model of Poincare sphere, which is then applied to the solution of some particular problems relevant in the line formation in a magnetic field.
Abstract: The general properties of the transfer equations for polarized radiation are discussed in detail and some relevant symmetries about the absorption matrix and the emission vector are deduced. A geometrical picture of the process of radiative transfer for polarized radiation is given by generalizing the model of the Poincare sphere. An «electromagnetic analogy» is achieved and it is then applied to the solution of some particular problems relevant in the process of line formation in a magnetic field.
TL;DR: In this article, the authors discuss the problem of generating two vastly different mass scales through spontaneous symmetry breaking and find that to all orders in perturbation theory this can only be achieved if there is a non-trivial relation between the couplings of the theory.