414 research outputs found
The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
We prove that the extended Poincare group in (1+1) dimensions is
non-nilpotent solvable exponential, and therefore that it belongs to type I. We
determine its first and second cohomology groups in order to work out a
classification of the two-dimensional relativistic elementary systems.
Moreover, all irreducible unitary representations of the extended Poincare
group are constructed by the orbit method. The most physically interesting
class of irreducible representations corresponds to the anomaly-free
relativistic particle in (1+1) dimensions, which cannot be fully quantized.
However, we show that the corresponding coadjoint orbit of the extended
Poincare group determines a covariant maximal polynomial quantization by
unbounded operators, which is enough to ensure that the associated quantum
dynamical problem can be consistently solved, thus providing a physical
interpretation for this particular class of representations.Comment: 12 pages, Revtex 4, letter paper; Revised version of paper published
in J. Math. Phys. 45, 1156 (2004
Semidirect products and the Pukanszky condition
We study the general geometrical structure of the coadjoint orbits of a
semidirect product formed by a Lie group and a representation of this group on
a vector space. The use of symplectic induction methods gives new insight into
the structure of these orbits. In fact, each coadjoint orbit of such a group is
obtained by symplectic induction on some coadjoint orbit of a "smaller" Lie
group. We study also a special class of polarizations related to a semidirect
product and the validity of Pukanszky's condition for these polarizations. Some
examples of physical interest are discussed using the previous methods.Comment: 33 pages, including special macros and fonts (JGPpaper.tex is the
source TeX file), to appear in J. Geom. Phys., also available via anonymous
ftp or via gopher gopher://cpt.univ-mrs.fr
Decreased oxygen permeability of EVOH through molecular interactions
Poly(ethylene-co-vinyl alcohol) of 48 mol% ethylene content was modified with N,N'-bis(2,2,6,6-tetramethyl-4-piperidyl)-isophthalamide (Nylostab SEED) to decrease the oxygen permeability of the polymer. The additive was added in a wide concentration range from 0 to 10 wt%. The structure and properties of the polymer were characterized with various methods including differential scanning calorimetry, X-ray diffraction, mechanical testing, optical measurements and oxygen permeation. Interactions were estimated by molecular modeling and infrared spectroscopy. The results showed that oxygen permeation decreased considerably when the additive was added at less than 2.0 wt% concentration. The decrease resulted from the interaction of the hydroxyl groups of the polymer and the amide groups of the additive. The dissolution of the additive in the polymer led to decreased crystallinity, but also to decreased mobility of amorphous molecules. Stiffness and strength, but also deformability increased as a result. Above 2 wt% the additive forms a separate phase leading to the deterioration of properties. The success of the approach represents a novel way to control oxygen permeation in EVOH and in other polymers with similar functional groups capable of strong interactions
Improvement of the impact resistance of natural fiber–reinforced polypropylene composites through hybridization
Polypropylene (PP) hybrid composites were prepared by the combination of naturalreinforcements and poly(ethylene terephthalate) (PET) fibers. Wood, flax, and sugarpalm fibers were used to increase stiffness and strength, while PET fibers served toimprove impact resistance. Interfacial adhesion was increased by using a maleated PP(MAPP) coupling agent. The hybrid composites containing 20 wt% of the naturalfibers were homogenized in a twin-screw compounder and then injection moldedinto standard tensile specimens. The amount of PET fibers was changed from 0 to40 wt% in the composites. Tensile and impact testing, acoustic emission measure-ments, and scanning electron microscopy (SEM) were used for the characterizationof the composites as well as to follow deformation and failure processes. The resultsproved that the concept of using PET fibers to improve impact resistance works withall natural fibers. Local deformations, the debonding or pullout of the PET fibers, initi-ate the plastic deformation of the matrix, which consumes considerable energy. Thefracture of PET fibers might also contribute to energy absorption. The type of naturalfiber does not influence the effect; the amount of PET fibers determines fractureresistance. The improvement of interfacial adhesion by coupling increases strengthand slightly improves impact resistance. The overall properties of the hybrid compos-ites prepared are acceptable, sufficiently large stiffness and impact resistance beingachieved for a large number of structural application
Plancherel formula for Berezin deformation of on Riemannian symmetric space
Consider the space B of complex matrces with norm <1. There
exists a standard one-parameter family of unitary representations of the
pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e.
scalar highest weight representations). Consider the restriction of
to the pseudoorthogonal group O(p,q).
The representation of O(p,q) in on the symmetric space
is a limit of the representations in some
precise sence. Spectrum of a representation is comlicated and it depends
on .
We obtain the complete Plancherel formula for the representations for
all admissible values of the parameter . We also extend this result to
all classical noncompact and compact Riemannian symmetric spaces
Notes on Stein-Sahi representations and some problems of non harmonic analysis
We discuss one natural class of kernels on pseudo-Riemannian symmetric
spaces.Comment: 40p
Stein--Sahi complementary series and their degenerations
The aim of the paper is an introduction to Stein--Sahi complementary series,
holomorphic series, and 'unipotent representations'. We also discuss some open
problems related to these objects. For the sake of simplicity, we consider only
the groups U(n,n).Comment: 40pp, 7fig, revised versio
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