437 research outputs found
Integration of twisted Dirac brackets
The correspondence between Poisson structures and symplectic groupoids,
analogous to the one of Lie algebras and Lie groups, plays an important role in
Poisson geometry; it offers, in particular, a unifying framework for the study
of hamiltonian and Poisson actions. In this paper, we extend this
correspondence to the context of Dirac structures twisted by a closed 3-form.
More generally, given a Lie groupoid over a manifold , we show that
multiplicative 2-forms on relatively closed with respect to a closed 3-form
on correspond to maps from the Lie algebroid of into the
cotangent bundle of , satisfying an algebraic condition and a
differential condition with respect to the -twisted Courant bracket. This
correspondence describes, as a special case, the global objects associated to
twisted Dirac structures. As applications, we relate our results to equivariant
cohomology and foliation theory, and we give a new description of
quasi-hamiltonian spaces and group-valued momentum maps.Comment: 42 pages. Minor changes, typos corrected. Revised version to appear
in Duke Math.
Linear and multiplicative 2-forms
We study the relationship between multiplicative 2-forms on Lie groupoids and
linear 2-forms on Lie algebroids, which leads to a new approach to the
infinitesimal description of multiplicative 2-forms and to the integration of
twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic
Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds
In this paper we investigate equivariant Morita theory for algebras with
momentum maps and compute the equivariant Picard groupoid in terms of the
Picard groupoid explicitly. We consider three types of Morita theory:
ring-theoretic equivalence, *-equivalence and strong equivalence. Then we apply
these general considerations to star product algebras over symplectic manifolds
with a Lie algebra symmetry. We obtain the full classification up to
equivariant Morita equivalence.Comment: 28 pages. Minor update, fixed typos
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star
products and their Picard groups. We point out the relations between
noncommutative field theories and deformed vector bundles which give the Morita
equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002.
Some typos fixe
Deformation Quantization of a Certain Type of Open Systems
We give an approach to open quantum systems based on formal deformation
quantization. It is shown that classical open systems of a certain type can be
systematically quantized into quantum open systems preserving the complete
positivity of the open time evolution. The usual example of linearly coupled
harmonic oscillators is discussed.Comment: Major update. Improved main statements. 21 page
Integration of Dirac-Jacobi structures
We study precontact groupoids whose infinitesimal counterparts are
Dirac-Jacobi structures. These geometric objects generalize contact groupoids.
We also explain the relationship between precontact groupoids and homogeneous
presymplectic groupoids. Finally, we present some examples of precontact
groupoids.Comment: 10 pages. Brief changes in the introduction. References update
Management of a pregnant woman with fibromuscular dysplasia
No abstract available
Techniques for an image space occlusion culling engine
In this work we present several techniques applied to implement an Image Space Software Occlusion Culling Engine to increase the speed of rendering general dynamic scenes with high depth complexity. This conservative culling method is based on a tiled Occlusion Map that is updated only when needed, deferring and even avoiding the expensive per pixel rasterization process. We show how the tiles become a useful way to increase the speed of visibility tests. Finally we describe how different parts of the engine were parallelized using OpenMP directives and SIMD instructions.Eje: Workshop Computación gráfica, imágenes y visualización (WCGIV)Red de Universidades con Carreras en Informática (RedUNCI
Gauged (2,2) Sigma Models and Generalized Kahler Geometry
We gauge the (2,2) supersymmetric non-linear sigma model whose target space
has bihermitian structure (g, B, J_{\pm}) with noncommuting complex structures.
The bihermitian geometry is realized by a sigma model which is written in terms
of (2,2) semi-chiral superfields. We discuss the moment map, from the
perspective of the gauged sigma model action and from the integrability
condition for a Hamiltonian vector field. We show that for a concrete example,
the SU(2) x U(1) WZNW model, as well as for the sigma models with almost
product structure, the moment map can be used together with the corresponding
Killing vector to form an element of T+T* which lies in the eigenbundle of the
generalized almost complex structure. Lastly, we discuss T-duality at the level
of a (2,2) sigma model involving semi-chiral superfields and present an
explicit example.Comment: 33 page
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