Showing papers on "Symmetry (physics) published in 1987"
TL;DR: In this paper, the effect of symmetry considerations on the deterministic deterministic design of coherent structures is discussed. But, as we will see in this part, symmetry considerations can considerably extend the amount of available data and can be significant in designing numerical or physical experiments.
Abstract: l. Introduction. The accurate determindtion of coherent structures depends upon having a sufficiently large database. As we will see in this part, symmetry considerations can considerably extend the amount of available data. In addition, a priori consideration of symmetries can be significant in designing numerical or physical experiments. In the following we outline, on a case by case basis, and sometimes only in brief, the effect of such deliberations for a number of standard geometries. We then show how such data can be transformed for use in related geometries.
1,002 citations
TL;DR: In this article, the relativistic Brueckner-Hartree-Fock approach for dense neutron matter is extended to dense dense matter and contributions arising from tensor interactions due to the exchange of π-and ϱ-mesons and the dependence upon neutron-proton asymmetry.
247 citations
TL;DR: In this article, the phase space approach to general relativity in the asymptotically flat context is reconsidered, phrasing it in the language of symplectic geometry, and the necessary boundary conditions at spatial infinity are spelled out in detail.
230 citations
TL;DR: In this article, a uniform description of free massless fields of all integer and half-integer spins s greater than or equal to 3/2 on an anti-de Sitter background is given.
Abstract: Linearized curvatures are constructed which allow a completely uniform description of free massless fields of all integer and half-integer spins sgreater than or equal to3/2 on an anti-de Sitter background. The corresponding action functionals and equations of motion are found. The proposed linearized curvatures specify the ''initial data'' for deriving a nonabelian symmetry corresponding to a (hypothetical) nontrivial theory of massless higher-spin fields interacting with gravity.
180 citations
TL;DR: In this article, a two-parameter family of various homology groups and cohomology groups of charge density contour surfaces is proposed for a detailed characterization of the shapes of electronic charge distributions of general, asymmetric molecules.
Abstract: A group theoretical framework is proposed for a detailed characterization of the shapes of electronic charge distributions of general, asymmetric molecules. The proposed shape groups are the homology and cohomology groups of charge density contour surfaces. These shape groups depend on two real parameters, the charge density value a for the contour and a curvature parameter b. The two-parameter family of various homology groups and cohomology groups of charge density contour surfaces is independent of the symmetry properties of the molecules and gives a concise description of the dominant shape characteristics. For any fixed parameter value b these groups may change only at specific charge density values, characteristic to the given molecule. On the other hand, for a fixed-charge density contour the group changes induced by a change in the curvature parameter b provide a description of the fine details of the shape of the electron density. The changes in the structure of these groups follow strict algebraic relations, that provide a quantitative measure for shape-similarity between various molecules. The two-parameter shape group method is an extension of an earlier method proposed for biochemical applications.
120 citations
101 citations
Book•
31 Jan 1987
TL;DR: The role and value of symmetry principles and Einstein's contribution to their recognition are discussed in this article. But the authors focus on the application of the symmetry principles to the atomic shell model of the Nucleus.
Abstract: Why We Believe in the Einstein Theory.- The Role and Value of the Symmetry Principles and Einstein's Contribution to Their Recognition.- Statistical Concepts in Einstein's Physics.- What Are the True Building Blocks of Matter.- Classification of Wigner Operators by a New Type of Weight Space Diagram.- De Sitter Fibers and SO(3,2) Spectrum Generating Group for Hadrons.- The Wigner-Racah Algebra for Finite and Compact Continuous Groups.- Applications of Coherent States in Thermodynamics and Dynamics.- The Application of Imbedding Theory to the Atomic Shell Model.- Group Theory in Atomic and Molecular Physics.- New Approach to Matrix Elements and Clebsch-Gordan Coefficients for Compact and Non-Compact Groups.- Group Theory and the Interaction of Composite Nucleon Systems.- Time Reversal in Dissipative Systems.- Life Groups, Quantum Mechanics, Many-Body Theory and Organic Chemistry.- Symmetry and Variable Separation for the Helmholtz, Wave and Hamilton-Jacobi Equations.- Review of the Group Theory behind the Interacting Boson Model of the Nucleus.- Remarks on the Algebraic Structure of Spontaneous Symmetry Breaking in Unified Gauge Theories.- Symmetry Breaking and Far-From-Equilibrium Order.- Finite Subgroups of the Lorentz Group and Their Generating Functions.- On Dynamical Symmetries in Relativistic Field Theories.- On the Generalisation of the Gell-Mann-Nishijima Relation.- Relativistic Dynamical Groups in Quantum Theory and Some Possible Applications.- Generalized Coherent States.- Spontaneous Symmetry Breaking in Bifurcation Problems.- Time, Energy, Relativity, and Cosmology.- Projection Operators for Semisimple Compact Lie Groups and Their Applications.- Orders in Nature: From Quantum to Classical.- Systematic Methods for Determining the Continuous Transformation Groups Admitted by Differential Equations.- Symmetry Breaking in Embryology and in Neurobiology.- On Global Properties of Quantum Systems.- Invited Speakers and Invited Participants.
94 citations
TL;DR: In this article, the vanishing of the one-loop string cosmological constant in nontrivial non supersymmetric backgrounds can be understood by viewing the path integral as an inner product of orthogonal wave functions.
90 citations
TL;DR: In this article, generic bifurcations of equilibria in one-parameter Hamiltonian systems with symmetry group Γ on the generalized eigenvalues of the linearized system go through zero.
88 citations
TL;DR: In this article, it was shown that if the local gauge symmetry of general relativity is broken, the singularity theorems may be evaded, and in particular the cosmological singularity of the standard model may be prevented, even if the gravitational sources satisfy the strong energy condition.
Abstract: It is shown that, if the local gauge symmetry of general relativity is broken, the singularity theorems may be evaded, and in particular the cosmological singularity of the standard model may be prevented, even if the gravitational sources satisfy the strong energy condition.
79 citations
TL;DR: In this paper, an analytic solution of the coherent evolution of a laser-driven N-level quantum system that possesses an SU(2) dynamic symmetry is presented, which is the same as the solution presented in this paper.
Abstract: We present an analytic solution of the coherent evolution of a laser-driven N-level quantum system that possesses an SU(2) dynamic symmetry.
TL;DR: In this article, a class of scale invariant σ -models on homogeneous spaces is presented and the symmetry properties of these models are discussed, and the central charge of the Virasoro algebra associated with the energymomentum tensor is computed at two loops.
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TL;DR: In this article, the authors introduce the characteristic symmetry function, based on the characteristic function of the underlying distribution, whose behaviour is indicative of symmetry or its absence, and propose a statistic for testing symmetry about an unspecified center, derived from the empirical characteristic symmetry functions.
Abstract: SUMMARY We introduce the characteristic symmetry function, based on the characteristic function of the underlying distribution, whose behaviour is indicative of symmetry or its absence. A statistic is proposed for testing symmetry about an unspecified centre, derived from the empirical characteristic symmetry function. The statistic is readily computible, it utilizes information in the empirical characteristic function over an interval, and does not require the estimation of the centre of symmetry. Under general symmetry the asymptotic null distribution of the statistic is folded normal. The empirical power for selected alternatives is studied by a small-scale simulation and a numerical illustration is given.
TL;DR: In this article, the Raman spectra of ordinary and extraordinary phonons in LiNbO3 and LiTaO3 are recorded under a set of angles between wave vector and optic axis with the same backward scattering geometry.
Abstract: Raman spectra of ordinary and extraordinary phonons in LiNbO3 and LiTaO3 are recorded under a set of angles between wave vector and optic axis with the same backward scattering geometry, which makes all of the extraordinary phonons to appear in one directional-dispersion spectra series, and the directional dispersion is reliably determined. The symmetry and the number of polar phonons in both the crystals are found to be the same, 4A1T + 4A1L + 9ET + 9EL. The directional dispersion of extraordinary phonons has thirteen branches with similar coupling in LiNbO3 and LiTaO3.
[Russian Text Ignored].
TL;DR: The algebraic dynamics of systems with long-range (instantaneous) interactions requires an enlargement of the local algebra which, in most relevant cases, includes variables at infinity that enter in an essential way in the time evolution of local variables.
Abstract: The algebraic dynamics of systems with long‐range (instantaneous) interactions requires an enlargement of the (quasi) local algebra which, in most relevant cases, includes variables at infinity that enter in an essential way in the time evolution of local variables. The mathematical structures emerging for the treatment of long‐range dynamics are investigated also in connection with spontaneous symmetry breaking.
TL;DR: In this paper, Type II superstrings are compactified to four dimensions giving rise to a dimension-18 semi-simple Lie group, which satisfies perturbative unitarity and is finite at least to one loop.
TL;DR: These equations do not contain the linear absorption coefficient, mu, explicitly so they are valid in principle for any mu, and are used to extend the work of Brahme, Roos, and Lax to dose distributions which are not circularly symmetrical.
Abstract: We give the equations which need to be solved to extend the work of Brahme, Roos, and Lax to dose distributions which are not circularly symmetrical. These equations do not contain the linear absorption coefficient, μ, explicitly so they are valid in principle for any μ. The general solution of these equations has not been found, but the solution given by Brahme, Roos, and Lax is used to extend their work to simple dose distributions with an axis of symmetry. Some examples are given and discussed.
TL;DR: In this paper, the Euler equations of 1-dimensional adiabatic gas dynamics with arbitrary equation of state were shown to have a symmetry S of order three, i.e. such that S3 = 1.
TL;DR: The local generators of symmetry transformations which have recently been constructed from a quantum field theoretical version of Noether's theorem are shown to converge to the global generators as the volume tends to the whole space.
Abstract: The local generators of symmetry transformations which have recently been constructed from a quantum field theoretical version of Noether's theorem are shown to converge to the global ones as the volume tends to the whole space. The proof relies on the continuous volume dependence of the universal localizing maps which are associated to the local splitW*-inclusions.
TL;DR: In this article, the symmetry properties of NH3 dimer are analyzed in the molecular symmetry group and the physical assumptions underlying the choice of this group are detailed, and several low lying tunneling states are predicted.
Abstract: The symmetry properties of NH3 dimer are analyzed in the molecular symmetry group and the physical assumptions underlying the choice of this group are detailed. Several low lying tunneling states are predicted. Two of these states transform as four‐dimensional (G) representations of G36, the molecular symmetry group. These two states can have the same microwave selection rules as those found in the two experimentally observed states of NH3 dimer. That is, the microwave transitions can follow pure rotational selection rules (no tunneling splittings) even though interchange tunneling is included as a feasible motion in the molecular symmetry group. The observation of these selection rules is interpreted as internal rotation stabilizing the system against interchange tunneling. Hence, in these particular states the interchange tunneling is quenched. The group theory predicts this picture of ammonia dimer to be appropriate if certain internal rotation interactions are large compared to the interchange tunneli...
TL;DR: In this article, the authors show how cancellations occur between contributions from different hadronic intermediate states to two-step OZI-violating transition amplitudes in which each individual step is OZI allowed.
TL;DR: All generalized soliton solutions of the Einstein-Rosen form in the cylindrical context are considered, based on the asymptotic behavior of the Riemann and metric tensors, the deficit angle, and a C-velocity associated to Thorne's C-energy.
Abstract: We consider all generalized soliton solutions of the Einstein-Rosen form in the cylindrical context. They are Petrov type-I solutions which describe solitonlike waves interacting with a line source placed on the symmetry axis. Some of the solutions develop a curvature singularity on the axis which is typical of massive line sources, whereas others just have the conical singularity revealing the presence of a static cosmic string. The analysis is based on the asymptotic behavior of the Riemann and metric tensors, the deficit angle, and a C-velocity associated to Thorne's C-energy. The C-energy is found to be radiated along the null directions.
TL;DR: In this paper, a non-linear thermodynamic model of heat-conducting anisotropic solid is elaborated which turns out to be in a conservative form, through the associated main field variables, the symmetry and the hyperbolicity properties are investigated.
Abstract: A non-linear thermodynamic model of heat-conducting anisotropic solid is elaborated which turns out to be in a conservative form. Then, through the associated main field variables, the symmetry and the hyperbolicity properties are investigated. As outstanding applications, the analysis of the grow of the wave discontinuities and the evaluation of the critical time are performed. Finally, the Rankine-Hugoniot conditions for the system of equations are given in detail.
TL;DR: In this paper, the gravitational field equations for a spherical symmetric perfect fluid were completely solved, and the general analytical solution depends on an arbitrary function of the radial coordinate of the fluid.
Abstract: The gravitational field equations for a spherical symmetric perfect fluid are completely solved The general analytical solution obtained depends on an arbitrary function of the radial coordinate As illustrations of the proposed procedure the exterior and interior Schwarzschild solutions are regained
TL;DR: The method is applied to a study of the basis-invariant conditions for CP symmetry with any number of families, where it is shown that the condition can immediately be written down in an invariant fashion, with the help of the projection operators.
Abstract: Basis-independent flavor projection operators are constructed from the quark mass matrices in the standard electroweak model. These operators keep track of the identity of the quarks in any arbitrary basis for the mass matrices. The method is applied to a study of the basis-invariant conditions for CP symmetry with any number of families, where it is shown that the condition can immediately be written down in an invariant fashion, with the help of the projection operators. For the case of 4 families the CP conditions are worked out in detail and their symmetry properties are exhibited, with the use of the appropriate reduction formulas. The question of mass degeneracies, which is essential in discussing CP symmetry, is also studied. Finally, for the case of 3 families, an invariant measure of CP violation is given.
TL;DR: In this article, the transformation properties of the Mueller matrix on application of certain spatial symmetry operations, partially combined with reversal of motion, to the sample (including the fields) can be given explicitly.
TL;DR: In this article, a matrix extension of the conventional recursion method was proposed to calculate the symmetry preserving inter-site Green function from a relatively small number of the recursion coefficients, or whenever the symmetry properties of the Green function is important.
Abstract: A new recursion algorithm which is free from symmetry difficulties in the resultant Green function associated with the axis rotation is developed as a straightforward matrix extension of the conventional recursion method of Haydock and co-workers (1975, 1980). The present method is particularly useful when one needs to calculate the symmetry preserving inter-site Green function from a relatively small number of the recursion coefficients, or whenever the symmetry properties of the Green function is important.
TL;DR: In this article, the authors present a model with continuous or discrete abelian generation group G, which predicts all orders of magnitude for fermion masses ad mixings correctly as a function of only one small parameter φSM ≈ 110.
TL;DR: In this paper, the kinematic properties of anisotropic fluids in general relativity that admit a conformal collineation, a generalization of conformal motion, are investigated.
Abstract: Anisotropic fluids in general relativity that admit a conformal collineation, a generalization of a conformal motion, are considered. By investigating the kinematic properties of such fluids, and then using the field equations, some recent results on the restrictions imposed by a conformal collineation symmetry are generalized.