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 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.

Zur Lösung der BETHE-GOLDSTONE-Gleichung bei nicht-verschwindendem Gesamtimpuls I

1963 ◽  
Vol 18 (4) ◽  
pp. 531-538
Author(s):  
Dallas T. Hayes
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Nuclear Matter ◽  
Analytical Solutions ◽  
Projection Operator ◽  
Center Of Mass ◽  
Separable Potential ◽  
Localized Solutions ◽  
Non Local ◽  
Square Well

Localized solutions of the BETHE—GOLDSTONE equation for two nucleons in nuclear matter are examined as a function of the center-of-mass momentum (c. m. m.) of the two nucleons. The equation depends upon the c. m. m. as parameter due to the dependence upon the c. m. m. of the projection operator appearing in the equation. An analytical solution of the equation is obtained for a non-local but separable potential, whereby a numerical solution is also obtained. An approximate solution for small c. m. m. is calculated for a square-well potential. In the range of the approximation the two analytical solutions agree exactly.

ANALYTIC SAMPLING APPROXIMATION BY PROJECTION OPERATOR WITH APPLICATION IN DECOMPOSITION OF INSTANTANEOUS FREQUENCY

2013 ◽  
Vol 11 (05) ◽  
pp. 1350040 ◽  
Author(s):  
YOUFA LI ◽  
TAO QIAN
Keyword(s):  
Hardy Space ◽  
Numerical Experiment ◽  
Hilbert Transform ◽  
Mild Condition ◽  
Instantaneous Frequency ◽  
Projection Operator ◽  
Approximation Scheme ◽  
Special Functions ◽  
Cauchy Kernel ◽  
Sequence Of Functions

A sequence of special functions in Hardy space [Formula: see text] are constructed from Cauchy kernel on unit disk 𝔻. Applying projection operator of the sequence of functions leads to an analytic sampling approximation to f, any given function in [Formula: see text]. That is, f can be approximated by its analytic samples in 𝔻s. Under a mild condition, f is approximated exponentially by its analytic samples. By the analytic sampling approximation, a signal in [Formula: see text] can be approximately decomposed into components of positive instantaneous frequency. Using circular Hilbert transform, we apply the approximation scheme in [Formula: see text] to Ls(𝕋2) such that a signal in Ls(𝕋2) can be approximated by its analytic samples on ℂs. A numerical experiment is carried out to illustrate our results.

Some Properties of Symplectic Manifolds S on the Projective Tangent Bundle PTM

2011 ◽  
Vol 187 ◽  
pp. 483-486
Author(s):  
Yong He ◽  
Xiao Ying Lu ◽  
Wei Na Lu
Keyword(s):  
Vector Field ◽  
Symplectic Manifold ◽  
Tangent Bundle ◽  
Fiber Bundle ◽  
Symplectic Manifolds ◽  
Lie Derivative ◽  
The Relationship

In this paper, we show the relationship between 2-form of the two projective tangent bundle and the relationship between 2-form on projective tangent bundle and 1-form on by using the theory of fiber bundle and the properties of symplectic manifold of the projective tangent bundle . Moreover, we derived a simpler formula of Lie derivative of a special vector field, which is on the projective tangent bundle.

scholarly journals A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow

2016 ◽  
Vol 139 ◽  
pp. 120-129 ◽  
Author(s):  
Sumedh M. Joshi ◽  
Peter J. Diamessis ◽  
Derek T. Steinmoeller ◽  
Marek Stastna ◽  
Greg N. Thomsen
Keyword(s):  
Projection Operator ◽  
Inviscid Flow ◽  
Processing Technique ◽  
Post Processing ◽  
Pressure Projection ◽  
Discontinuous Pressure
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