1,374 research outputs found

    Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions

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    As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of the status of the program by addressing some frequently asked questions. This account is addressed primarily to researchers outside the loop quantum gravity community.Comment: 21 pages, to appear in the Proceedings of the 11th Marcel Grossmann Conferenc

    Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory

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    We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the noncommutativity scale. The effective field theory can also contain higher-curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described.Comment: 31 pages LaTeX; References adde

    A conceptual problem for non-commutative inflation and the new approach for non-relativistic inflationary equation of state

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    In a previous paper, we connected the phenomenological non-commutative inflation of Alexander, Brandenberger and Magueijo (2003) and Koh S and Brandenberger (2007) with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group like procedure in which even Hopf algebras (roughly the symmetries of non-commutative spaces) could lead to the equation of state of inflationary radiation. In this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons is bounded from above) and the group structure of the representation which leads to the fundamental inflationary equations of state. We show that such a group structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like in scattering theory, for example. Therefore, it follows that the procedure to obtain those equations should be modified according to one of two possible proposals that we consider here. One of them relates to the general theory of Hopf algebras while the other is based on a representation theorem of Von Neumann algebras, a proposal already suggested by us to take into account interactions in the inflationary equation of state. This reopens the problem of finding inflationary deformed dispersion relations and all developments which followed the first paper of Non-commutative Inflation.Comment: Phys. Rev. D, 2013, in pres

    Representations of quantum conjugacy classes of orthosymplectic groups

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    Let GG be the complex symplectic or special orthogonal group and \g its Lie algebra. With every point xx of the maximal torus TGT\subset G we associate a highest weight module MxM_x over the Drinfeld-Jimbo quantum group U_q(\g) and a quantization of the conjugacy class of xx by operators in \End(M_x). These quantizations are isomorphic for xx lying on the same orbit of the Weyl group, and MxM_x support different representations of the same quantum conjugacy class.Comment: 19 pages, no figure

    Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media

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    In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and other physical objects. Particularly interesting are dynamical models invariant under the group underlying geometry of degrees of freedom. In contrary to the single body case there exist nontrivial potentials invariant under this group (left and right acting). The concept of relative (mutual) deformation tensors of pairs of affine bodies is discussed. Scalar invariants built of such tensors are constructed. There is an essential novelty in comparison to deformation scalars of single affine bodies, i.e., there exist affinely-invariant scalars of mutual deformations. Hence, the hierarchy of interaction models according to their invariance group, from Euclidean to affine ones, can be considered.Comment: 50 pages, 4 figure

    Geospatial images in the acquisition of spatial knowledge for wayfinding

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    Geospatial images such as maps and aerial photographs are important sources of spatial knowledge that people use for wayfinding. The rapid development of geodata acquisition and digital graphics has recently led to rather complete geographic coverage of both traditional and novel types of geospatial images. Divergent types of geospatial images vary in their support of human acquisition of spatial knowledge. However evaluative studies about the acquisition of spatial knowledge from the diversity of geospatial images have been rare. In this article we review a variety of literature about the acquisition of spatial knowledge while paying particular attention to the role of geospatial images. Based on the literature we present a framework of image parameters that characterize the acquisition of spatial knowledge from geospatial images: vantage point number of visible vertical features and visual realism. With the help of the framework we evaluate commonly used geospatial images. In concordance with the previous experiments our evaluation shows that the different types of geospatial images have large differences in the types of spatial knowledge they support and to what extent. However further experimentation is needed in order to better understand the human cognitive needs for geospatial images and to develop more useful geospatial images for wayfinding

    Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory

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    We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.Comment: 70 pages, 4 figures; v2: References added and update
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