scholarly journals Noncommutative differential calculus for Moyal subalgebras

2006 ◽  
Vol 56 (4) ◽  
pp. 611-622 ◽  
Author(s):  
G. Marmo ◽  
P. Vitale ◽  
A. Zampini
Keyword(s):  
Differential Calculus ◽  
Noncommutative Differential Calculus

Noncommutative Differential Calculus and Its Application on Discrete Spaces

2008 ◽  
Vol 49 (1) ◽  
pp. 37-44
Author(s):  
Liu Zhen ◽  
Bai Yong-Qiang ◽  
Wu Ke ◽  
Guo Han-Ying
Keyword(s):  
Differential Calculus ◽  
Discrete Spaces ◽  
Noncommutative Differential Calculus

CARTAN CALCULUS OF Z3-GRADED DIFFERENTIAL CALCULUS ON THE QUANTUM PLANE

2012 ◽  
Vol 09 (05) ◽  
pp. 1250040
Author(s):  
ERDOĜAN MEHMET ÖZKAN
Keyword(s):  
Differential Calculus ◽  
Quantum Plane ◽  
Lie Derivatives ◽  
Noncommutative Differential Calculus

To give a Z3-graded Cartan calculus on the extended quantum plane, the noncommutative differential calculus on the extended quantum plane is extended by introducing inner derivations and Lie derivatives.

DEFORMED HARMONIC OSCILLATOR AND NONLINEAR COHERENT STATES: NONCOMMUTATIVE QUANTUM SPACE APPROACH

2009 ◽  
Vol 24 (10) ◽  
pp. 1963-1986 ◽  
Author(s):  
MOHAMMAD HOSSEIN NADERI ◽  
MAHMOOD SOLTANOLKOTABI ◽  
RASOUL ROKNIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Differential Calculus ◽  
Quantum Plane ◽  
Quantum Harmonic Oscillator ◽  
Commutation Relations ◽  
Noncommutative Differential Calculus ◽  
Two Parameter ◽  
Noncommutative Quantum ◽  
Space Approach

In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.

Noncommutative Differential Calculus Approach to Discrete Symplectic Schemes on Regular Lattice

2000 ◽  
Vol 34 (2) ◽  
pp. 307-316 ◽  
Author(s):  
Guo HanYing ◽  
Wu Ke ◽  
Wang ShangHu ◽  
Wang ShiKun ◽  
Wei GongMin
Keyword(s):  
Differential Calculus ◽  
Regular Lattice ◽  
Noncommutative Differential Calculus ◽  
Symplectic Schemes
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