Coherent states in the form of a quantum group

1993 ◽  
Vol 32 (4) ◽  
pp. 545-553 ◽  
Author(s):  
Lei Ma ◽  
Zhong Tang ◽  
Yong-de Zhang
Keyword(s):  
Quantum Group ◽  
Coherent States

scholarly journals COHERENT STATES, DYNAMICS AND SEMICLASSICAL LIMIT ON QUANTUM GROUPS

1994 ◽  
Vol 09 (08) ◽  
pp. 689-703 ◽  
Author(s):  
I. YA. AREF'EVA ◽  
R. PARTHASARATHY ◽  
K. S. VISWANATHAN ◽  
I. V. VOLOVICH
Keyword(s):  
Representation Theory ◽  
Quantum Group ◽  
Quantum Groups ◽  
Crucial Role ◽  
Coherent States ◽  
Semiclassical Limit ◽  
Time Variable ◽  
Weyl Quantization ◽  
Algebra Of Functions

Coherent states on the quantum group SU q(2) are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit q → 1 is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to q-deformation as a q-Weyl quantization and a relevance of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.

Noncommutative Structure of Quantum Group Coherent States

2009 ◽  
Author(s):  
N. Aizawa ◽  
R. Chakrabarti ◽  
Swee-Ping Chia ◽  
Kurunathan Ratnavelu ◽  
Muhamad Rasat Muhamad
Keyword(s):  
Quantum Group ◽  
Coherent States

Gazeau- Klouder Coherent states on a sphere

2019 ◽  
Vol 19 (2) ◽  
pp. 379-390
Author(s):  
Z Heibati ◽  
A Mahdifar ◽  
E Amooghorban ◽  
◽  
◽  
...  
Keyword(s):  
Coherent States

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

sl(2)-modules bysl(2)-coherent states

2016 ◽  
Vol 57 (9) ◽  
pp. 091704 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Coherent States
Sign in / Sign up

Export Citation Format

Share Document