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
1994 ◽  
Vol 09 (08) ◽  
pp. 689-703 ◽  
Author(s):  
I. YA. AREF'EVA ◽  
R. PARTHASARATHY ◽  
K. S. VISWANATHAN ◽  
I. V. VOLOVICH

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.


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

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

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba

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.


Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau

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.


2016 ◽  
Vol 57 (9) ◽  
pp. 091704 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  

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