Projection Operator Method and Q-Analog of Angular Momentum Theory

Smirnov, Yu.F.; Tolstoy, V. N.; Kharitonov, Yu.I.

doi:10.1007/978-1-4615-3696-3_24

Cited by 16 publications

(72 citation statements)

References 7 publications

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“…iv) 3n-j symbols (with n=1, 2, 3, 4, 5) for su q (2) can be found in 100 . v) The q-deformed version of the Wigner-Eckart theorem can be found in 101,102,103 . vi) Irreducible tensor operators for su q (2) can be found in 103 .…”

Section: Wkb-eps For the Q-deformed Oscillatormentioning

confidence: 99%

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Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)⊃so (3) model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator and its relation to the nuclear shell model, the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to the structure of molecules and of atomic clusters, as well as an outlook are also given.

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Section: Wkb-eps For the Q-deformed Oscillatormentioning

confidence: 99%

“…v) The q-deformed version of the Wigner-Eckart theorem can be found in 101,102,103 . vi) Irreducible tensor operators for su q (2) can be found in 103 . In addition, it should be noticed that a two-parameter deformation of su(2), labelled as su p,q (2) has been introduced 51,53,104,105,106,107,108 .…”

Section: Wkb-eps For the Q-deformed Oscillatormentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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“…The classical Wigner-Racah definition of the irreducible tensor operator has been extented to the quantum lie algebras in papers [6,7,10] and Wigner-Eckart theorem has been proved in the similar way as in classical undeformed symmetry structures. In papers [11,12] a new, more general definitions of tensor operators for arbitrary Hopf algebra has been proposed.…”

Section: Introductionmentioning

confidence: 98%

Tensor operators and Wigner–Eckart theorem for the quantum superalgebraU_q[osp(1|2)]

Mozrzymas¹

2004

J. Phys. A: Math. Gen.

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“…Indeed, we have since the generators A r 12 and A32 commute and since A r 12 P U = δr,0P U . We now consider the application of the generator A32 to the projection operator P U : ¿From here on, we use the commutation relations from [7,25] for generators raised to a power. In view of the relation P U +1/2 A21 = (A12P U +1/2 ) + = 0, the application of this operator on the projection operator P U +1/2 from the left yields As a result, the square of the norm becomes …”

Section: Resultsmentioning

confidence: 99%

“…The noncompact u q (2, 1) quantum algebra is also specified by nine generators A ik (i, k = 1, 2, 3) satisfying the same commutation relations as the generators of the u q (3) compact quantum algebra. The explicit expressions for these commutators can be found in [7]. As to their properties with respect to Hermitian conjugation, those in (4) and (6) remain valid, whereas, in view of the relations…”

Section: Positive Discrete Series Of Unitary Irreducible Representationsmentioning

confidence: 99%

Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations

Smirnov

Kharitonov²

Symmetries in Science XI

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The structure positive of unitary irreducible representations of the noncompact uq(2, 1) quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the suq(2) subalgebra, a q-analog of the Gel'fand-Graev formulas is derived in the basis corresponding to the reduction uq(2, 1) → suq(2) × u(1). Projection operators for the suq(1, 1) subalgebra are employed to study the same representations for the reduction uq(2, 1) → u(1) × suq(1, 1). The matrix elements of the generators of the uq(2, 1) algebra are computed in this new basis. A general analytic expression for an element of the transformation bracket U |T q between the bases associated with above two reductions (the elements of this matrix are referred to as q-Weyl coefficients) is obtained for a general case where the deformation parameter q is not equal to a root of unity. It is shown explicitly that, apart from a phase, q-Weyl coefficients coincide with the q-Racah coefficients for the suq(2) quantum algebra.

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Projection Operator Method and Q-Analog of Angular Momentum Theory

Cited by 16 publications

References 7 publications

Quantum groups and their applications in nuclear physics

Quantum groups and their applications in nuclear physics

Tensor operators and Wigner–Eckart theorem for the quantum superalgebraU_q[osp(1|2)]

Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations

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Projection Operator Method and Q-Analog of Angular Momentum Theory

Cited by 16 publications

References 7 publications

Quantum groups and their applications in nuclear physics

Quantum groups and their applications in nuclear physics

Tensor operators and Wigner–Eckart theorem for the quantum superalgebraUq[osp(1|2)]

Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations

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Tensor operators and Wigner–Eckart theorem for the quantum superalgebraU_q[osp(1|2)]