scholarly journals Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
P. Hurtado ◽  
A. Leones ◽  
J. B. Moreno
Keyword(s):  
Deformation Quantization ◽  
Integral Transform ◽  
Geometric Quantization ◽  
Strict Quantization ◽  
Standard Techniques ◽  
Real Polarization

Using standard techniques from geometric quantization, we rederive the integral product of functions on ℝ2 (non-Euclidian) which was introduced by Pierre Bieliavsky as a contribution to the area of strict quantization. More specifically, by pairing the nontransverse real polarization on the pair groupoid ℝ2×ℝ¯2, we obtain the well-defined integral transform. Together with a convolution of functions, which is a natural deformation of the usual convolution of functions on the pair groupoid, this readily defines the Bieliavsky product on a subset of L2ℝ2.

KLAUDER’S QUANTIZATION IN THE ALMOST-KAEHLER CASE

1992 ◽  
Vol 07 (15) ◽  
pp. 1377-1380
Author(s):  
P. MARANER ◽  
E. ONOFRI ◽  
G.P. TECCHIOLLI
Keyword(s):  
Symplectic Manifold ◽  
Projection Operator ◽  
Geometric Quantization ◽  
Real Polarization

We prove that a regularized projection operator on the physical subspace ℋ phys ⊂ℒ2(Ω) can be defined for a symplectic manifold Ω=T*M equipped with an “Almost-Kaehler” structure, provided that a suitable counterterm is added to Klauder’s definition. The present result extends Klauder’s quantization to the case in which geometric quantization requires a real polarization.

scholarly journals QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS

2005 ◽  
Vol 17 (04) ◽  
pp. 391-490 ◽  
Author(s):  
S. TWAREQUE ALI ◽  
MIROSLAV ENGLIŠ
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Deformation Quantization ◽  
Degrees Of Freedom ◽  
Geometric Quantization ◽  
Canonical Quantization ◽  
Open Problems ◽  
General Picture ◽  
The Subject

This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics, Segal and Borel quantizations, geometric quantization, various ramifications of deformation quantization, Berezin and Berezin–Toeplitz quantizations, prime quantization and coherent state quantization. We have attempted to give an account sufficiently in depth to convey the general picture, as well as to indicate the mutual relationships between various methods, their relative successes and shortcomings, mentioning also open problems in the area. Finally, even for approaches for which lack of space or expertise prevented us from treating them to the extent they would deserve, we have tried to provide ample references to the existing literature on the subject. In all cases, we have made an effort to keep the discussion accessible both to physicists and to mathematicians, including non-specialists in the field.

INVERSE SQUARE ROOT MOMENT SINGULARITIES IN RECTANGULAR PLATES CONTAINING AN INTERNAL LINE SUPPORT

2009 ◽  
Vol 06 (01) ◽  
pp. 1-21 ◽  
Author(s):  
YOS SOMPORNJAROENSUK ◽  
KRAIWOOD KIATTIKOMOL
Keyword(s):  
Strain Energy ◽  
Integral Transform ◽  
Internal Line ◽  
Square Root ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Partial Support ◽  
Uniform Loading ◽  
Dual Series Equations ◽  
Standard Techniques

Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.

scholarly journals DEFORMATION QUANTIZATION OF COADJOINT ORBITS

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2397-2400 ◽  
Author(s):  
M. A. LIEDÓ
Keyword(s):  
Lie Groups ◽  
Algebraic Structure ◽  
Deformation Quantization ◽  
Geometric Quantization ◽  
Coadjoint Orbits ◽  
Semisimple Lie Groups

A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.

Pathogenesis of Human Hair Defects

1974 ◽  
Vol 32 ◽  
pp. 12-13
Author(s):  
P.S. Porter ◽  
T. Aoyagi ◽  
R. Matta
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Human Hair ◽  
Standard Techniques ◽  
Scanning Electron

Using standard techniques of scanning electron microscopy (SEM), over 1000 human hair defects have been studied. In several of the defects, the pathogenesis of the abnormality has been clarified using these techniques. It is the purpose of this paper to present several distinct morphologic abnormalities of hair and to discuss their pathogenesis as elucidated through techniques of scanning electron microscopy.

A non-cyanide method of electropolishing silver

1978 ◽  
Vol 36 (1) ◽  
pp. 146-147
Author(s):  
R. L. Lyles ◽  
S. J. Rothman ◽  
W. Jäger
Keyword(s):  
Electron Microscopy ◽  
Sulphuric Acid ◽  
Methyl Alcohol ◽  
Health Hazards ◽  
Silver Alloy ◽  
High Quality ◽  
Silver Alloys ◽  
Free Sample ◽  
Specimen Quality ◽  
Standard Techniques

Standard techniques of electropolishing silver and silver alloys for electron microscopy in most instances have relied on various CN recipes. These methods have been characteristically unsatisfactory due to difficulties in obtaining large electron transparent areas, reproducible results, adequate solution lifetimes, and contamination free sample surfaces. In addition, there are the inherent health hazards associated with the use of CN solutions. Various attempts to develop noncyanic methods of electropolishing specimens for electron microscopy have not been successful in that the specimen quality problems encountered with the CN solutions have also existed in the previously proposed non-cyanic methods.The technique we describe allows us to jet polish high quality silver and silver alloy microscope specimens with consistant reproducibility and without the use of CN salts.The solution is similar to that suggested by Myschoyaev et al. It consists, in order of mixing, 115ml glacial actic acid (CH3CO2H, specific wt 1.04 g/ml), 43ml sulphuric acid (H2SO4, specific wt. g/ml), 350 ml anhydrous methyl alcohol, and 77 g thiourea (NH2CSNH2).

Fine structure and possible functions of the hermaphrodite duct of some pulmonate snails (Mollusca: Gastropoda)

1990 ◽  
Vol 48 (3) ◽  
pp. 68-69
Author(s):  
Alan N. Hodgson
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Fine Structure ◽  
Seminal Vesicle ◽  
Reproductive Biology ◽  
Light Microscope ◽  
Light Microscope Level ◽  
Transmission Electron ◽  
Standard Techniques

The hermaphrodite duct of pulmonate snails connects the ovotestis to the fertilization pouch. The duct is typically divided into three zones; aproximal duct which leaves the ovotestis, the middle duct (seminal vesicle) and the distal ovotestis duct. The seminal vesicle forms the major portion of the duct and is thought to store sperm prior to copulation. In addition the duct may also play a role in sperm maturation and degredation. Although the structure of the seminal vesicle has been described for a number of snails at the light microscope level there appear to be only two descriptions of the ultrastructure of this tissue. Clearly if the role of the hermaphrodite duct in the reproductive biology of pulmonatesis to be understood, knowledge of its fine structure is required.Hermaphrodite ducts, both containing and lacking sperm, of species of the terrestrial pulmonate genera Sphincterochila, Levantina, and Helix and the marine pulmonate genus Siphonaria were prepared for transmission electron microscopy by standard techniques.

Microstructural observations of the “Wustite-Spinel” coexistence following quenching of cation-excess spinels, Ni2(1+x)Ti1-xO4

1990 ◽  
Vol 48 (4) ◽  
pp. 1058-1059
Author(s):  
Ian M. Anderson ◽  
Arnulf Muan ◽  
C. Barry Carter
Keyword(s):  
Film Growth ◽  
Spinel Phase ◽  
Model Systems ◽  
Ion Milling ◽  
Coexistence Of Phases ◽  
Nonequilibrium Conditions ◽  
Diffraction Patterns ◽  
Spinel Structures ◽  
Highly Porous ◽  
Standard Techniques

Oxide mixtures which feature a coexistence of phases with the wüstite and spinel structures are considered model systems for the study of solid-state reaction kinetics, phase boundaries, and thin-film growth, and such systems are especially suited to TEM studies. (In this paper, the terms “wüstite” and “spinel” will refer to phases of those structure types.) The study of wüstite-spinel coexistence has been limited mostly to systems near their equilibrium condition, where the assumptions of local thermodynamic equilibrium are valid. The cation-excess spinels of the type Ni2(1+x)Ti1-xO4, which reportedly exist only above 1375°C4, provide an excellent system for the study of wüstite-spinel coexistence under highly nonequilibrium conditions. The nature of these compounds has been debated in the literature. X-ray and neutron powder diffraction patterns have been used to advocate the existence of a single-phase, non- stoichiometric spinel. TEM studies of the microstructure have been used to suggest equilibrium coexistence of a stoichiometric spinel, Ni2TiO4, and a wüstite phase; this latter study has shown a coexistence of wüstite and spinel phases in specimens thought to have been composed of a single, non- stoichiometric spinel phase. The microstructure and nature of this phase coexistence is the focus of this study. Specimens were prepared by ball-milling a mixture of NiO and TiO2 powders with 10 wt.% TiO2. The mixture was fired in air at 1483°C for 5 days, and then quenched to room temperature. The aggregate thus produced was highly porous, and needed to be infiltrated prior to TEM sample preparation, which was performed using the standard techniques of lapping, dimpling, and ion milling.

Sign in / Sign up

Export Citation Format

Share Document