17,199 research outputs found
On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes
It is shown that the large limit of SU(N) YM in -dim
backgrounds can be subsumed by a higher dimensional gravitational theory
which can be identified to an -dim generally invariant gauge theory of diffs
, where is an -dim internal space (Cho, Sho, Park, Yoon). Based on
these findings, a very plausible geometrical interpretation of the
correspondence could be given. Conformally invariant sigma models in
dimensions with target non-compact SO(2n,1) groups are reviewed. Despite the
non-compact nature of the SO(2n,1), the classical action and Hamiltonian are
positive definite. Instanton field configurations are found to correspond
geometrically to conformal ``stereographic'' mappings of into the
Euclidean signature spaces. The relation between Self Dual branes
and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion
on symmetry is given and we outline the Vasiliev procedure to
construct an action involving higher spin massless fields in . This
spacetime higher spin theory should have a one-to-one correspondence to
noncritical strings propagating on .Comment: 43 pages, Tex fil
The orientation-preserving diffeomorphism group of S^2 deforms to SO(3) smoothly
Smale proved that the orientation-preserving diffeomorphism group of S^2 has
a continuous strong deformation retraction to SO(3). In this paper, we
construct such a strong deformation retraction which is diffeologically smooth.Comment: 16 page
Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach
Cardiac motion estimation is an important diagnostic tool to detect heart
diseases and it has been explored with modalities such as MRI and conventional
ultrasound (US) sequences. US cardiac motion estimation still presents
challenges because of the complex motion patterns and the presence of noise. In
this work, we propose a novel approach to estimate the cardiac motion using
ultrafast ultrasound data. -- Our solution is based on a variational
formulation characterized by the L2-regularized class. The displacement is
represented by a lattice of b-splines and we ensure robustness by applying a
maximum likelihood type estimator. While this is an important part of our
solution, the main highlight of this paper is to combine a low-rank data
representation with topology preservation. Low-rank data representation
(achieved by finding the k-dominant singular values of a Casorati Matrix
arranged from the data sequence) speeds up the global solution and achieves
noise reduction. On the other hand, topology preservation (achieved by
monitoring the Jacobian determinant) allows to radically rule out distortions
while carefully controlling the size of allowed expansions and contractions.
Our variational approach is carried out on a realistic dataset as well as on a
simulated one. We demonstrate how our proposed variational solution deals with
complex deformations through careful numerical experiments. While maintaining
the accuracy of the solution, the low-rank preprocessing is shown to speed up
the convergence of the variational problem. Beyond cardiac motion estimation,
our approach is promising for the analysis of other organs that experience
motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201
Contact structures, deformations and taut foliations
Using deformations of foliations to contact structures as well as rigidity
properties of Anosov foliations we provide infinite families of examples which
show that the space of taut foliations in a given homotopy class of plane
fields is in general not path connected. Similar methods also show that the
space of representations of the fundamental group of a hyperbolic surface to
the group of smooth diffeomorphisms of the circle with fixed Euler class is in
general not path connected. As an important step along the way we resolve the
question of which universally tight contact structures on Seifert fibered
spaces are deformations of taut or Reebless foliations when the genus of the
base is positive or the twisting number of the contact structure in the sense
of Giroux is non-negative.Comment: 37 pages, 2 figures; Improved exposition incorporating referee's
comments mainly in Sections 5 and 9. (To appear in Geom. Topol.
Wick type deformation quantization of Fedosov manifolds
A coordinate-free definition for Wick-type symbols is given for symplectic
manifolds by means of the Fedosov procedure. The main ingredient of this
approach is a bilinear symmetric form defined on the complexified tangent
bundle of the symplectic manifold and subject to some set of algebraic and
differential conditions. It is precisely the structure which describes a
deviation of the Wick-type star-product from the Weyl one in the first order in
the deformation parameter. The geometry of the symplectic manifolds equipped by
such a bilinear form is explored and a certain analogue of the
Newlander-Nirenberg theorem is presented. The 2-form is explicitly identified
which cohomological class coincides with the Fedosov class of the Wick-type
star-product. For the particular case of K\"ahler manifold this class is shown
to be proportional to the Chern class of a complex manifold. We also show that
the symbol construction admits canonical superextension, which can be thought
of as the Wick-type deformation of the exterior algebra of differential forms
on the base (even) manifold. Possible applications of the deformed superalgebra
to the noncommutative field theory and strings are discussed.Comment: 20 pages, no figure
Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras
-algebraic Weyl quantization is extended by allowing also degenerate
pre-symplectic forms for the Weyl relations with infinitely many degrees of
freedom, and by starting out from enlarged classical Poisson algebras. A
powerful tool is found in the construction of Poisson algebras and
non-commutative twisted Banach--algebras on the stage of measures on the not
locally compact test function space. Already within this frame strict
deformation quantization is obtained, but in terms of Banach--algebras
instead of -algebras. Fourier transformation and representation theory of
the measure Banach--algebras are combined with the theory of continuous
projective group representations to arrive at the genuine -algebraic
strict deformation quantization in the sense of Rieffel and Landsman. Weyl
quantization is recognized to depend in the first step functorially on the (in
general) infinite dimensional, pre-symplectic test function space; but in the
second step one has to select a family of representations, indexed by the
deformation parameter . The latter ambiguity is in the present
investigation connected with the choice of a folium of states, a structure,
which does not necessarily require a Hilbert space representation.Comment: This is a contribution to the Special Issue on Deformation
Quantization, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
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