8,976 research outputs found
Groupoid Quantization of Loop Spaces
We review the various contexts in which quantized 2-plectic manifolds are
expected to appear within closed string theory and M-theory. We then discuss
how the quantization of a 2-plectic manifold can be reduced to ordinary
quantization of its loop space, which is a symplectic manifold. We demonstrate
how the latter can be quantized using groupoids. After reviewing the necessary
background, we present the groupoid quantization of the loop space of R^3 in
some detail.Comment: 19 pages, Proceedings of the Corfu Summer Institute 2011 - School and
Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011,
Corfu, Greec
Branes, Quantization and Fuzzy Spheres
We propose generalized quantization axioms for Nambu-Poisson manifolds, which
allow for a geometric interpretation of n-Lie algebras and their enveloping
algebras. We illustrate these axioms by describing extensions of
Berezin-Toeplitz quantization to produce various examples of quantum spaces of
relevance to the dynamics of M-branes, such as fuzzy spheres in diverse
dimensions. We briefly describe preliminary steps towards making the notion of
quantized 2-plectic manifolds rigorous by extending the groupoid approach to
quantization of symplectic manifolds.Comment: 18 pages; Based on Review Talk at the Workshop on "Noncommutative
Field Theory and Gravity", Corfu Summer Institute on Elementary Particles and
Physics, September 8-12, 2010, Corfu, Greece; to be published in Proceedings
of Scienc
The 2-Hilbert Space of a Prequantum Bundle Gerbe
We construct a prequantum 2-Hilbert space for any line bundle gerbe whose
Dixmier-Douady class is torsion. Analogously to usual prequantisation, this
2-Hilbert space has the category of sections of the line bundle gerbe as its
underlying 2-vector space. These sections are obtained as certain morphism
categories in Waldorf's version of the 2-category of line bundle gerbes. We
show that these morphism categories carry a monoidal structure under which they
are semisimple and abelian. We introduce a dual functor on the sections, which
yields a closed structure on the morphisms between bundle gerbes and turns the
category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert
spaces fit various expectations from higher prequantisation. We then extend the
transgression functor to the full 2-category of bundle gerbes and demonstrate
its compatibility with the additional structures introduced. We discuss various
aspects of Kostant-Souriau prequantisation in this setting, including its
dimensional reduction to ordinary prequantisation.Comment: 97 pages; v2: minor changes; Final version to be published in Reviews
in Mathematical Physic
Lightning Imaging Sensor (LIS) for the Earth Observing System
Not only are scientific objectives and instrument characteristics given of a calibrated optical LIS for the EOS but also for the Tropical Rainfall Measuring Mission (TRMM) which was designed to acquire and study the distribution and variability of total lightning on a global basis. The LIS can be traced to a lightning mapper sensor planned for flight on the GOES meteorological satellites. The LIS consists of a staring imager optimized to detect and locate lightning. The LIS will detect and locate lightning with storm scale resolution (i.e., 5 to 10 km) over a large region of the Earth's surface along the orbital track of the satellite, mark the time of occurrence of the lightning, and measure the radiant energy. The LIS will have a nearly uniform 90 pct. detection efficiency within the area viewed by the sensor, and will detect intracloud and cloud-to-ground discharges during day and night conditions. Also, the LIS will monitor individual storms and storm systems long enough to obtain a measure of the lightning flashing rate when they are within the field of view of the LIS. The LIS attributes include low cost, low weight and power, low data rate, and important science. The LIS will study the hydrological cycle, general circulation and sea surface temperature variations, along with examinations of the electrical coupling of thunderstorms with the ionosphere and magnetosphere, and observations and modeling of the global electric circuit
Cheeger-Simons differential characters with compact support and Pontryagin duality
By adapting the Cheeger-Simons approach to differential cohomology, we
establish a notion of differential cohomology with compact support. We show
that it is functorial with respect to open embeddings and that it fits into a
natural diagram of exact sequences which compare it to compactly supported
singular cohomology and differential forms with compact support, in full
analogy to ordinary differential cohomology. We prove an excision theorem for
differential cohomology using a suitable relative version. Furthermore, we use
our model to give an independent proof of Pontryagin duality for differential
cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125
(2003) 791]: On any oriented manifold, ordinary differential cohomology is
isomorphic to the smooth Pontryagin dual of compactly supported differential
cohomology. For manifolds of finite-type, a similar result is obtained
interchanging ordinary with compactly supported differential cohomology.Comment: 33 pages, no figures - v3: Final version to be published in
Communications in Analysis and Geometr
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
Differential cohomology and locally covariant quantum field theory
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C*-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr\'echet-Lie group structure on differential cohomology groups
- …