3,589 research outputs found
Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
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
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
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
We extract the Weyl scalars and 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 , and
one of the phases (the product 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
corresponds to a global constant mass parameter that equals the ADM mass (or,
equivalently in perturbation theory, that or equal their values in
the no-radiation limits), thus determining the two moduli of the Weyl scalars
, while leaving their phases as yet undetermined. Second,
we break the spin symmetry by requiring that the ratio 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 and perturbatively in the quasi-Kinnersley tetrad.Comment: 13 page
A New Spin Foam Model for 4d Gravity
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
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
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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