3,589 research outputs found

    Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity

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    We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier in [arXiv:0705.0674], we show that the EPR model realizes a consistent imposition of the simplicity constraints implementing general relativity from a topological BF theory.Comment: 6 pages, 2 figures, v2: typos correcte

    Spinor representation of surfaces and complex stresses on membranes and interfaces

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    Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.Comment: 17 page

    The second order local-image-structure solid

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    Characterization of second order local image structure by a 6D vector ( or jet) of Gaussian derivative measurements is considered. We consider the affect on jets of a group of transformations - affine intensity-scaling, image rotation and reflection, and their compositions - that preserve intrinsic image structure. We show how this group stratifies the jet space into a system of orbits. Considering individual orbits as points, a 3D orbifold is defined. We propose a norm on jet space which we use to induce a metric on the orbifold. The metric tensor shows that the orbifold is intrinsically curved. To allow visualization of the orbifold and numerical computation with it, we present a mildly-distorting but volume-preserving embedding of it into euclidean 3-space. We call the resulting shape, which is like a flattened lemon, the second order local-image-structure solid. As an example use of the solid, we compute the distribution of local structures in noise and natural images. For noise images, analytical results are possible and they agree with the empirical results. For natural images, an excess of locally 1D structure is found

    Towards a wave-extraction method for numerical relativity. V. Extracting the Weyl scalars in the quasi-Kinnersley tetrad from spatial data

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    We extract the Weyl scalars Ψ0\Psi_0 and Ψ4\Psi_4 in the quasi-Kinnersley tetrad by finding initially the (gauge--, tetrad--, and background--independent) transverse quasi-Kinnersley frame. This step still leaves two undetermined degrees of freedom: the ratio Ψ0/Ψ4|\Psi_0|/|\Psi_4|, and one of the phases (the product Ψ0Ψ4|\Psi_0|\cdot |\Psi_4| and the {\em sum} of the phases are determined by the so-called BB radiation scalar). The residual symmetry ("spin/boost") can be removed by gauge fixing of spin coefficients in two steps: First, we break the boost symmetry by requiring that ρ\rho corresponds to a global constant mass parameter that equals the ADM mass (or, equivalently in perturbation theory, that ρ\rho or μ\mu equal their values in the no-radiation limits), thus determining the two moduli of the Weyl scalars Ψ0,Ψ4|\Psi_0|, |\Psi_4|, while leaving their phases as yet undetermined. Second, we break the spin symmetry by requiring that the ratio π/τ\pi/\tau gives the expected polarization state for the gravitational waves, thus determining the phases. Our method of gauge fixing--specifically its second step--is appropriate for cases for which the Weyl curvature is purely electric. Applying this method to Misner and Brill--Lindquist data, we explicitly find the Weyl scalars Ψ0\Psi_0 and Ψ4\Psi_4 perturbatively in the quasi-Kinnersley tetrad.Comment: 13 page

    A New Spin Foam Model for 4d Gravity

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    Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4d Riemannian quantum gravity that generalises the well-known Barrett-Crane model and resolves the inherent to it ultra-locality problem. The BF formulation of 4d gravity possesses two sectors: gravitational and topological ones. The model presented here is shown to give a quantization of the gravitational sector, and is dual to the recently proposed spin foam model of Engle et al. which, we show, corresponds to the topological sector. Our methods allow us to introduce the Immirzi parameter into the framework of spin foam quantisation. We generalize some of our considerations to the Lorentzian setting and obtain a new spin foam model in that context as well.Comment: 40 pages; (v2) published versio

    Rigidity of infinitesimal momentum maps

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    In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.Peer ReviewedPostprint (updated version

    Rigidity of infinitesimal momentum maps

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    In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.Comment: 16 page
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