1,673 research outputs found
Fuzzy Surfaces of Genus Zero
A fuzzy version of the ordinary round 2-sphere has been constructed with an
invariant curvature. We here consider linear connections on arbitrary fuzzy
surfaces of genus zero. We shall find as before that they are more or less
rigidly dependent on the differential calculus used but that a large number of
the latter can be constructed which are not covariant under the action of the
rotation group. For technical reasons we have been forced to limit our
considerations to fuzzy surfaces which are small perturbations of the fuzzy
sphere.Comment: 11 pages, Late
Linear Connections on Fuzzy Manifolds
Linear connections are introduced on a series of noncommutative geometries
which have commutative limits. Quasicommutative corrections are calculated.Comment: 10 pages PlainTex; LPTHE Orsay 95/42; ESI Vienna 23
A Dynamical 2-dimensional Fuzzy Space
The noncommutative extension of a dynamical 2-dimensional space-time is given
and some of its properties discussed. Wick rotation to euclidean signature
yields a surface which has as commutative limit the doughnut but in a singular
limit in which the radius of the hole tends to zero.Comment: 13 pages, accepted for publication in Phys. Lett.
The Energy-momentum of a Poisson structure
Consider the quasi-commutative approximation to a noncommutative geometry. It
is shown that there is a natural map from the resulting Poisson structure to
the Riemann curvature of a metric. This map is applied to the study of
high-frequency gravitational radiation. In classical gravity in the WKB
approximation there are two results of interest, a dispersion relation and a
conservation law. Both of these results can be extended to the noncommutative
case, with the difference that they result from a cocycle condition on the
high-frequency contribution to the Poisson structure, not from the field
equations.Comment: 22 page
Quantization of a gauge theory on a curved noncommutative space
We study quantization of a gauge analogon of the Grosse-Wulkenhaar model: we
find divergent one-loop contributions to the 1-point and 2-point Green
functions. We obtain that five counterterms are necessary for renormalization
and that all divergences are logarithmic.Comment: 23 pages, 3 figure
High Resolution Rotation Curves of Low Surface Brightness Galaxies
High resolution Halpha rotation curves are presented for five low surface
brightness galaxies. These Halpha rotation curves have shapes different from
those previously derived from HI observations, probably because of the higher
spatial resolution of the Halpha observations. The Halpha rotation curves rise
more steeply in the inner parts than the HI rotation curves and reach a flat
part beyond about two disk scale lengths. With radii expressed in optical disk
scale lengths, the rotation curves of the low surface brightness galaxies
presented here and those of HSB galaxies have almost identical shapes. Mass
modeling shows that the contribution of the stellar component to the rotation
curves may be scaled to explain most of the inner parts of the rotation curves,
albeit with high stellar mass-to-light ratios. On the other hand, well fitting
mass models can also be obtained with lower contributions of the stellar disk.
These observations suggest that the luminous mass density and the total mass
density are coupled in the inner parts of these galaxies.Comment: Accepted for publication in ApJ Letter
Can noncommutativity resolve the Big-Bang singularity?
A possible way to resolve the singularities of general relativity is proposed
based on the assumption that the description of space-time using commuting
coordinates is not valid above a certain fundamental scale. Beyond that scale
it is assumed that the space-time has noncommutative structure leading in turn
to a resolution of the singularity. As a first attempt towards realizing the
above programme a modification of the Kasner metric is constructed which is
commutative only at large time scales. At small time scales, near the
singularity, the commutation relations among the space coordinates diverge. We
interpret this result as meaning that the singularity has been completely
delocalized.Comment: Latex, 13 pages, 2 figures, accepted for publication in EPJ
Linear connections on matrix geometries
A general definition of a linear connection in noncommutative geometry has
been recently proposed. Two examples are given of linear connections in
noncommutative geometries which are based on matrix algebras. They both possess
a unique metric connection.Comment: 14p, LPTHE-ORSAY 94/9
Topology at the Planck Length
A basic arbitrariness in the determination of the topology of a manifold at
the Planck length is discussed. An explicit example is given of a `smooth'
change in topology from the 2-sphere to the 2-torus through a sequence of
noncommuting geometries. Applications are considered to the theory of D-branes
within the context of the proposed (atrix) theory.Comment: Orsay Preprint 97/34, 17 pages, Late
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