THE JORDAN-SCHWINGER REALIZATION OF TWO-PARAMETRIC QUANTUM GROUP slq,s(2)

1993 ◽  
Vol 08 (06) ◽  
pp. 543-548 ◽  
Author(s):  
SICONG JING
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Commutation Relations ◽  
Deformed Oscillator ◽  
Contraction Procedure

The Jordan-Schwinger realization of two-parametric quantum group sl q,s(2), is presented by introducing two-parametric deformed harmonic oscillator. The Heisenberg commutation relations of the two-parametric deformed oscillator are derived by virtue of the Schwinger’s contraction procedure.

scholarly journals Socles of Verma modules in quantum groups

1993 ◽  
Vol 47 (2) ◽  
pp. 221-231
Author(s):  
A.V. Jeyakumar ◽  
P.B. Sarasija
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Verma Modules ◽  
Commutation Relations

In this paper the Verma modules Me(λ) over the quantum group vε(sl(n + 1), ℂ), where ε is a primitive lth root of 1 are studied. Some commutation relations among the generators of Ue are obtained. Using these relations, it is proved that the socle of Mε(λ) is non-zero.

scholarly journals DIRAC OPERATORS ON QUANTUM-TWO SPHERES

1994 ◽  
Vol 09 (25) ◽  
pp. 2325-2333 ◽  
Author(s):  
KAZUTOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
Angular Momentum ◽  
Dirac Operator ◽  
Quantum Group ◽  
Total Angular Momentum ◽  
Dirac Operators ◽  
Wave Functions ◽  
Commutation Relations ◽  
Pauli Matrices

We investigate the spin-1/2 fermions on quantum-two spheres. It is shown that the wave functions of fermions and a Dirac operator on quantum-two spheres can be constructed in a manifestly covariant way under the quantum group SU (2)q. The concept of total angular momentum and chirality can be expressed by using q-analog of Pauli-matrices and appropriate commutation relations.

q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SUq(2) AND SUq(1, 1)

1990 ◽  
Vol 05 (04) ◽  
pp. 237-242 ◽  
Author(s):  
HARUO UI ◽  
N. AIZAWA
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Symmetry Group ◽  
Quantum Groups ◽  
Heisenberg Algebra ◽  
Positive Definiteness ◽  
Two Dimensional ◽  
Number Operator ◽  
Boson Operator ◽  
Dynamical Group

We propose a defining set of commutation relations to a q-analogue of boson operator; [Formula: see text], [Formula: see text] and [N, aq]=−aq, which contracts to the Heisenberg algebra of boson operators in the limit of q=1. Here, N is the number operator, [N]q being its q-analogue operator. By making use of this set, we construct a new realization of the “noncompact” quantum group SUq(1, 1) in addition to that of the SUq(2) recently proposed by Biedenharn. The explicit form of the number operator is given in terms of aq and [Formula: see text] and its positive definiteness is proved. A uniqueness of our commutators is also discussed. It is shown that the quantum group SUq(2) appears as a true symmetry group of a q-analogue of the two-dimensional harmonic oscillator and the SUq(1, 1) as its dynamical group.

QUANTUM GROUP SUq(2) FOR COMPLEX q-DEFORMATION

1995 ◽  
Vol 10 (36) ◽  
pp. 2783-2791 ◽  
Author(s):  
RAMANDEEP S. JOHAL ◽  
RAJ K. GUPTA
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Deformation Parameter ◽  
Molecular Physics ◽  
Special Cases ◽  
Arbitrary Complex ◽  
Physics Problems

q-deformed harmonic oscillator is established for any arbitrary complex q-deformation parameter (with real and imaginary q as its special cases) and the formalism so developed is used to construct the quantum group SUq(2). The eigenvalues of the Casimir of SUq(2) are now real, even for complex q-deformation (q=ea+ib). This happens for (a,b)≪1. Thus, the use of real part of energies in the earlier works of Gupta and collaborators7–14 is mathematically rigorous, since only small values of (a, b) are involved in all the nuclear and molecular physics problems studied7–14,18–20 so far.

Dependence of the r.m.s. nuclear radius on the deformation parameters

1969 ◽  
Vol 47 (11) ◽  
pp. 1189-1193 ◽  
Author(s):  
R. Y. Cusson ◽  
B. Castel
Keyword(s):  
Harmonic Oscillator ◽  
Experimental Studies ◽  
Oscillator Model ◽  
Nuclear Radius ◽  
Isotope Shifts ◽  
Deformation Parameters ◽  
Deformed Oscillator ◽  
Harmonic Oscillator Model ◽  
Natural Way ◽  
Oscillator Models

The concept of "nuclear compressibility under deformation", introduced by Fradkin and others in their experimental studies of isotope shifts, is analyzed. It is shown that in the harmonic-oscillator model Fradkin's compressibility parameter ξ can occur in a natural way. Theoretical estimates of ξ are obtained, using spherical and deformed oscillator models, as ξ = −5/4π and −5/16π respectively. They bracket the experimental value [Formula: see text]. Possible improvements of these estimates are discussed.

scholarly journals Quantum E(2) groups for complex deformation parameters

2021 ◽  
pp. 2150021
Author(s):  
Atibur Rahaman ◽  
Sutanu Roy
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Locally Compact ◽  
Complex Deformation ◽  
Circle Group ◽  
Deformation Parameters ◽  
Quantum Analogue ◽  
Group Contraction ◽  
Contraction Procedure ◽  
Matrix Formula

We construct a family of [Formula: see text] deformations of E(2) group for nonzero complex parameters [Formula: see text] as locally compact braided quantum groups over the circle group [Formula: see text] viewed as a quasitriangular quantum group with respect to the unitary [Formula: see text]-matrix [Formula: see text] for all [Formula: see text]. For real [Formula: see text], the deformation coincides with Woronowicz’s [Formula: see text] groups. As an application, we study the braided analogue of the contraction procedure between [Formula: see text] and [Formula: see text] groups in the spirit of Woronowicz’s quantum analogue of the classic Inönü–Wigner group contraction. Consequently, we obtain the bosonization of braided [Formula: see text] groups by contracting [Formula: see text] groups.

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