A Friedmann universe in the quantization scheme of reduced phase space

Astrophysics ◽  
1997 ◽  
Vol 40 (1) ◽  
pp. 83-93
Author(s):  
Yu. G. Palii ◽  
V. V. Papoyan ◽  
V. N. Pervushin
Keyword(s):  
Phase Space ◽  
Quantization Scheme ◽  
Friedmann Universe

Quantization scheme based on the extension of phase space

1993 ◽  
Vol 26 (3) ◽  
pp. 751-763 ◽  
Author(s):  
G Jorjadze ◽  
G Lavrelashvili ◽  
I Sarishvili
Keyword(s):  
Phase Space ◽  
Quantization Scheme

𝔓-quantization, 𝔔-quantization and Weyl quantization of a ray in classical phase space

2014 ◽  
Vol 29 (17) ◽  
pp. 1450069
Author(s):  
Rui He ◽  
Feng Chen ◽  
Hong-Yi Fan
Keyword(s):  
Phase Space ◽  
Pure State ◽  
Quantum Mechanical ◽  
Intermediate Representation ◽  
Weyl Quantization ◽  
Quantization Scheme ◽  
Classical Phase Space

By examining three quantization schemes of a ray function in classical phase space (a geometric ray is expressed by δ(x-λq-νp)), we find that the Weyl quantization scheme can reasonably demonstrate the correspondence between classical functions and quantum mechanical operators, since δ(x-λq-νp) really maps onto the operator δ(x-λQ-νP), where [Q, P] = iℏ, and δ(x-λQ-νP) represents a pure state (the coordinate-momentum intermediate representation), while 𝔓-ordered, 𝔔-ordered quantization schemes δ(x-λq-νp) to two different Fresnel integration kernels in Weyl-ordered form. Thus, Weyl quantization is more reasonable and preferable.

scholarly journals Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 787 ◽  
Author(s):  
Hervé Bergeron ◽  
Jean-Pierre Gazeau
Keyword(s):  
Phase Space ◽  
Large Family ◽  
Quantization Scheme ◽  
Integral Calculus ◽  
Integral Means ◽  
Weyl Transform ◽  
Quantization Maps ◽  
Singular Functions ◽  
Unitary Transformations ◽  
Symmetric Operators

Any quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all resources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. We first review this quantization scheme before revisiting the cases where symmetry covariance is described by the Weyl-Heisenberg group and the affine group respectively, and we emphasize the fundamental role played by Fourier transform in both cases. As an original outcome of our generalisations of the Wigner-Weyl transform, we show that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

PHASE-SPACE CONSIDERATIONS IN THE TRANSVERSE MOMENTUM ANALYSIS

1987 ◽  
Vol 48 (C2) ◽  
pp. C2-233-C2-239
Author(s):  
P. DANIELEWICZ
Keyword(s):  
Phase Space ◽  
Transverse Momentum

QUANTAL VERSUS CLASSICAL PHASE-SPACE DYNAMICS OF HEAVY-ION REACTIONS

1987 ◽  
Vol 48 (C2) ◽  
pp. C2-185-C2-194
Author(s):  
W. CASSING
Keyword(s):  
Phase Space ◽  
Heavy Ion ◽  
Heavy Ion Reactions ◽  
Space Dynamics ◽  
Classical Phase Space

Phase space of mechanical systems with a gauge group

1991 ◽  
Vol 161 (2) ◽  
pp. 13-75 ◽  
Author(s):  
Lev V. Prokhorov ◽  
Sergei V. Shabanov
Keyword(s):  
Phase Space ◽  
Gauge Group ◽  
Mechanical Systems

Numerical Study on Particle Distribution in Longitudinal Phase Space and Beam Current Profile using Compact Electron Beam Simulator for Heavy Ion Inertial Fusion

2017 ◽  
Vol 137 (5) ◽  
pp. 344-348
Author(s):  
Takashi Kikuchi ◽  
Yasuo Sakai ◽  
Jun Hasegawa ◽  
Kazuhiko Horioka ◽  
Kazumasa Takahashi ◽  
...  
Keyword(s):  
Electron Beam ◽  
Phase Space ◽  
Particle Distribution ◽  
Numerical Study ◽  
Heavy Ion ◽  
Beam Current ◽  
Inertial Fusion ◽  
Current Profile ◽  
Longitudinal Phase
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