1,374 research outputs found
Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions
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
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory
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
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
Let be the complex symplectic or special orthogonal group and \g its
Lie algebra. With every point of the maximal torus we
associate a highest weight module over the Drinfeld-Jimbo quantum group
U_q(\g) and a quantization of the conjugacy class of by operators in
\End(M_x). These quantizations are isomorphic for lying on the same orbit
of the Weyl group, and 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
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
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
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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