Tensorial structure of a q-deformed sp(4,R) superalgebra

Georgieva, A. I.; Dankova, Ts.

doi:10.1088/0305-4470/27/4/018

Cited by 8 publications

(11 citation statements)

References 26 publications

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“…Raychev, and R.P. Roussev (all from Bulgaria) developed a model based on a one-parameter deformation of SU (2) for dealing with rotational bands of deformed nuclei and rotational spectra of molecules [59] (see also [60]). Along the same line, a student of mine, R. Barbier, developed in his thesis a two-parameter deformation of SU (2) with application to superdeformed nuclei in mass region A ∼ 130−150 and A ∼ 190 [61].…”

Section: Some Personal Reminiscencesmentioning

confidence: 99%

In memoriam Yurii Fedorovich Smirnov: Some personal reminiscences on a great physicist

Kibler

2012

Phys. Atom. Nuclei

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Yurii Fedorovich Smirnov (1935-2008 was a famous theoretical physicist. He achieved his career mainly at the Institute of Nuclear Physics of Moscow. These notes describe some particular facets of the contributions of the late Professor Smirnov in theoretical physics and mathematical physics. They also relate some personal reminiscences on Yurii Smirnov in connection with some of his numerous works.

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Section: Some Personal Reminiscencesmentioning

confidence: 99%

In memoriam Yurii Fedorovich Smirnov: Some personal reminiscences on a great physicist

Kibler

2012

Phys. Atom. Nuclei

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“…Thus the degeneracy is eliminated in the same way as in the nondeformed case. Now the spaces in which the irreducible boson representations of the classical u ± (1, 1) and q-deformed u ± q (1, 1) act are the same and the decompositions (16) are the same, as we have…”

Section: Its Eigenvalues Equation Has the Formmentioning

confidence: 99%

“…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%

“…For completeness we present all the other commutation relations of the tensor operators (32), (33), and (34) in a slightly different form than in [15]. The commutators of L 1 ±1 with the pair raising and lowering operators define their transformation properties in respect to the q-deformed so(3) subalgebra:…”

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

confidence: 99%

“…Actually this is a general property of this tensor deformation of sp(4, R) because of the appearance of the q −2J 0 → q→1 1 factors on the right-hand-side of all commutation relations. The problem of eliminating this is solved in [16]. Working in terms of tensor operators makes the evaluation of the most general sp t (4, R) invariant operator with respect to the q-deformed so(3) subalgebra quite simple.…”

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

confidence: 99%

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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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