SO q (N) covariant differential calculus on quantum space and quantum deformation of schr�dinger equation

1991 ◽  
Vol 49 (3) ◽  
pp. 439-446 ◽  
Author(s):  
U. Carow-Watamura ◽  
M. Schlieker ◽  
S. Watamura
Keyword(s):  
Differential Calculus ◽  
Quantum Deformation ◽  
Quantum Space ◽  
Dinger Equation

scholarly journals COMMENT ON THE DIFFERENTIAL CALCULUS ON THE QUANTUM EXTERIOR PLANE

1998 ◽  
Vol 13 (20) ◽  
pp. 1645-1651 ◽  
Author(s):  
SALIH ÇELIK ◽  
SULTAN A. ÇELIK ◽  
METIN ARIK
Keyword(s):  
Symmetry Group ◽  
Differential Calculus ◽  
Baxter Equation ◽  
Oscillator Algebra ◽  
Quantum Deformation ◽  
R Matrix ◽  
Two Parameter ◽  
Parameter Deformation

We give a two-parameter quantum deformation of the exterior plane and its differential calculus without the use of any R-matrix and relate it to the differential calculus with the R-matrix. We prove that there are two types of solutions of the Yang–Baxter equation whose symmetry group is GL p,q(2). We also give a two-parameter deformation of the fermionic oscillator algebra.

scholarly journals DIFFERENTIAL CALCULI ON h-DEFORMED BOSONIC AND FERMIONIC QUANTUM PLANES

1993 ◽  
Vol 08 (39) ◽  
pp. 3741-3748 ◽  
Author(s):  
TATSUO KOBAYASHI
Keyword(s):  
Differential Calculus ◽  
Quantum Space

We study differential calculus on h-deformed bosonic and fermionic quantum space. It is shown that the fermionic quantum space involves a parafermionic variable as well as a classical fermionic one. Further we construct the classical su(2) algebra on the fermionic quantum space and discuss a mapping between the classical su(2) and the h-deformed su(2) algebras.

GAUGE THEORY ON A FOUR-DIMENSIONAL QUANTUM SPACE

2006 ◽  
Vol 21 (30) ◽  
pp. 2323-2330 ◽  
Author(s):  
M. EL BAZ
Keyword(s):  
Gauge Theory ◽  
Differential Calculus ◽  
Quantum Space

In this paper, a generalization and extension of some recent results is proposed. Namely, a four-dimensional quantum space is constructed and a differential calculus, obeying the usual criteria of covariance, is built upon this space. These results are then used to construct a gauge theory on this four-dimensional quantum space.

Differential calculus onN-dimensional quantum space

1994 ◽  
Vol 109 (3) ◽  
pp. 239-245 ◽  
Author(s):  
Won-Sang Chung
Keyword(s):  
Differential Calculus ◽  
Quantum Space

scholarly journals QUANTUM DEFORMATION OF igl(n) ALGEBRA ON QUANTUM SPACE

1996 ◽  
Vol 11 (07) ◽  
pp. 535-543
Author(s):  
TATSUO KOBAYASHI ◽  
HARU-TADA SATO
Keyword(s):  
Quantum Deformation ◽  
Quantum Space

We study quantum deformed gl(n) and igl(n) algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed gl(n) and igl(n) algebras by a quantum fermionic space. We investigate a map between deformed igl(2) algebras of our basis and other basis.

EXCITON INSULATOR STATES IN MATERIALS WITH ‘MEXICAN HAT’ BAND STRUCTURE DISPERSION AND IN GRAPHENE

2015 ◽  
Vol 11 (1) ◽  
pp. 2927-2949
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Band Structure ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Electron Hole ◽  
Dinger Equation ◽  
Fermi Sphere ◽  
Zinc Blende ◽  
Bulk Gan ◽  
Structure Dispersion ◽  
Excitonic States

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in grapheneand in materials with "Mexican hat" band structure dispersion as well as in zinc-blende GaN is presented. An integral twodimensionalSchrödinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection isexactly solved. The solutions of Schrödinger equation in momentum space in studied materials by projection the twodimensionalspace of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensionalSchrödinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. Instudied materials the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and lightabsorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole areseparated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materialsallows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone andhence driving the Cooper instability. The solutions of Coulomb problem of electron-hole pair does not depend from a widthof band gap of graphene. It means the absolute compliance with the cyclic geometry of diagrams at justification of theequation of motion for a microscopic dipole of graphene where >1 s r . The absorption spectrums for the zinc-blendeGaN/(Al,Ga)N quantum well as well as for the zinc-blende bulk GaN are presented. Comparison with availableexperimental data shows good agreement.

Сonanical quantum space-time and the arrow time

2020 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Space Time ◽  
Quantum Space

Сonanical quantum space-time and the arrow time

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