10,623 research outputs found
Algebras from Slightly Broken Higher Spin Symmetries
We define a class of -algebras that are obtained by deformations of
higher spin symmetries. While higher spin symmetries of a free CFT form an
associative algebra, the slightly broken higher spin symmetries give rise to a
minimal -algebra extending the associative one. These
-algebras are related to non-commutative deformation quantization
much as the unbroken higher spin symmetries result from the conventional
deformation quantization. In the case of three dimensions there is an
additional parameter that the -structure depends on, which is to be
related to the Chern-Simons level. The deformations corresponding to the
bosonic and fermionic matter lead to the same -algebra, thus
manifesting the three-dimensional bosonization conjecture. In all other cases
we consider, the -deformation is determined by a generalized free
field in one dimension lower.Comment: 48 pages, some pictures; typos fixed, presentation improve
Twisted submanifolds of R^n
We propose a general procedure to construct noncommutative deformations of an
embedded submanifold of determined by a set of smooth
equations . We use the framework of Drinfel'd twist deformation of
differential geometry of [Aschieri et al., Class. Quantum Gravity 23 (2006),
1883]; the commutative pointwise product is replaced by a (generally
noncommutative) -product determined by a Drinfel'd twist. The twists we
employ are based on the Lie algebra of vector fields that are tangent
to all the submanifolds that are level sets of the ; the twisted Cartan
calculus is automatically equivariant under twisted tangent infinitesimal
diffeomorphisms. We can consistently project a connection from the twisted
to the twisted if the twist is based on a suitable Lie
subalgebra . If we endow with a metric
then twisting and projecting to the normal and tangent vector fields commute,
and we can project the Levi-Civita connection consistently to the twisted ,
provided the twist is based on the Lie subalgebra
of the Killing vector fields of the metric; a
twisted Gauss theorem follows, in particular. Twisted algebraic manifolds can
be characterized in terms of generators and polynomial relations. We present in
some detail twisted cylinders embedded in twisted Euclidean and
twisted hyperboloids embedded in twisted Minkowski [these are
twisted (anti-)de Sitter spaces ].Comment: Latex file, 48 pages, 1 figure. Slightly adapted version to the new
preprint arXiv:2005.03509, where the present framework is specialized to
quadrics and other algebraic submanifolds of R^n. Several typos correcte
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
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
The generation of dual wavelength pulse fiber laser using fiber bragg grating
A stable simple generation of dual wavelength pulse fiber laser on experimental method is proposed and demonstrated by using Figure eight circuit diagram. The generation of dual wavelength pulse fiber laser was proposed using fiber Bragg gratings (FBGs) with two different central wavelengths which are 1550 nm and 1560 nm. At 600 mA (27.78 dBm) of laser diode, the stability of dual wavelength pulse fiber laser appears on 1550 nm and 1560 nm with the respective peak powers of -54.03 dBm and -58.00 dBm. The wavelength spacing of the spectrum is about 10 nm while the signal noise to ratio (SNR) for both peaks are about 8.23 dBm and 9.67 dBm. In addition, the repetition rate is 2.878 MHz with corresponding pulse spacing of about 0.5 Îźs, is recorded
Decoherence, the measurement problem, and interpretations of quantum mechanics
Environment-induced decoherence and superselection have been a subject of
intensive research over the past two decades, yet their implications for the
foundational problems of quantum mechanics, most notably the quantum
measurement problem, have remained a matter of great controversy. This paper is
intended to clarify key features of the decoherence program, including its more
recent results, and to investigate their application and consequences in the
context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio
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