Quantum groups and the recovery of U(3) symmetry in the Hamiltonian of the nuclear shell model

Mesa, Antonio del Sol; Loyola, G.; Moshińsky, M.; Velázquez, Víctor

doi:10.1088/0305-4470/26/5/033

Cited by 19 publications

(14 citation statements)

References 12 publications

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“…iii) Pan 263 and Del Sol Mesa et al 264 attacked the problem through the use of q-deforming functionals of secs 10, 14.…”

Section: The So Q (3) Limitmentioning

confidence: 99%

“…27 has been studied by Cseh 277 , Gupta 278 , and Del Sol Mesa et al 264 . Cseh 277 started with the su q (2) (vibrational) limit (in a form different from the one used in sec.…”

Section: The Question Of Complete Breaking Of Symmetries and Some Appmentioning

confidence: 99%

“…He noted that for q being a phase factor a recovery of the su(3) symmetry occurs (see also the next paragraph), while for real q, and even better for q complex (q = e s with s = a + ib), the so q (3) limit is indeed reached. Del Sol Mesa et al 264 considered the o q (3) limit of the model of sec. 27, since it corresponds to the symmetry of a q-deformed version of the spherical Nilsson Hamiltonian with spin-orbit coupling term.…”

Section: The Question Of Complete Breaking Of Symmetries and Some Appmentioning

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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“…iii) Pan 263 and Del Sol Mesa et al 264 attacked the problem through the use of q-deforming functionals of secs 10, 14.…”

Section: The So Q (3) Limitmentioning

confidence: 99%

“…27 has been studied by Cseh 277 , Gupta 278 , and Del Sol Mesa et al 264 . Cseh 277 started with the su q (2) (vibrational) limit (in a form different from the one used in sec.…”

Section: The Question Of Complete Breaking Of Symmetries and Some Appmentioning

confidence: 99%

Section: The Question Of Complete Breaking Of Symmetries and Some Appmentioning

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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“…This sp t (4, R) algebra [16] is decomposed in a natural way into a deformed compact subalgebra h = su t (2) ⊗ u t (1) that is generated by the spherical [18] as isomorphic by construction to a deformation of so(3) -the classical algebra of the angular momentum. Using the q-deformed realization [14] of the Clebsh-Gordon coefficients for su q (2) (23), we obtain the explicit expressions for the operators (32), ( 33) and (34) in terms of the q-spinors (29) and (30):…”

Section: Deformation In Terms Of Su Q (2) Tensor Operatorsmentioning

confidence: 99%

“…It must be noted that in this case those are deformed operators and do not have expression in terms of the classical bosons unlike the boson number operators N 1 and N −1 , used in the case of sp q (4, R). By means of an expansion like that introduced in (18) it is easy to verify the mixing of two kinds of oscillators k = ±1 introduced through the use of tensor operators…”

Section: Deformation In Terms Of Su Q (2) Tensor Operatorsmentioning

confidence: 99%

Deformations of the bosonsp(4,R) representation and its subalgebras

Draayer

Georgieva

Ivanov

2001

J. Phys. A: Math. Gen.

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The boson representation of the sp(4, R) algebra and two distinct deformations of it, spq (4, R) and spt(4, R), are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space, H, which is reducible into two irreducible representations acting in the subspaces H + and H − of H.The deformed representation of spq (4, R) is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4, R) (compact u(2) and noncompact u ε (1, 1) with ε = 0, ±) are also deformed and their deformed representations are contained in spq (4, R). They are reducible in the H + and H − spaces and decompose into irreducible representations. In this way a full description of the irreducible unitary representations of uq (2) of the deformed ladder series u 0 q (1, 1) and of two deformed discrete series u ± q (1, 1) are obtained. The other deformed representation, spt(4, R), is realized by means of a transformation of the qdeformed bosons into q-tensors (spinor-like) with respect to the suq (2) operators. All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, a deformed sut(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation in H is reducible and decomposes into irreducible ones that yields a complete description of the same.The basis states in H + , which require two quantum labels, are expressed in terms of three of the generators of the sp(4, R) algebra and are labeled by three linked integer parameters.

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