q-deformed Lie algebras and fractional calculus
نویسنده
چکیده
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool e.g. to describe the ground state spectra of even-even nuclei. In addition, the equivalence of rotational and vibrational spectra for fractional q-deformed Lie algebras is shown and the Bα(E2) values for the fractional q-deformed symmetric rotor are calculated. PACS numbers: 21.60.Fw, 21.10.k
منابع مشابه
Certain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators
The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...
متن کاملq-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...
متن کامل3 v 1 1 9 N ov 1 99 2 GL q ( N ) - Covariant Quantum Algebras and Covariant Differential Calculus ∗
We consider GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrari-ness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is dissc...
متن کاملIsomorphisms between Quantum Group Covariant q - Oscillator Systems Defined for q and q − 1
It is shown that there exists an isomorphism between q-oscillator systems covariant under SUq(n) and SUq−1(n). By the isomorphism, the defining relations of SUq−1(n) covariant q-oscillator system are transmuted into those of SUq(n). It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup SUq(n/m). Furthermore the cases of q-def...
متن کاملQuantum algebras and quivers
Given a finite quiver Q without loops, we introduce a new class of quantum algebras D(Q) which are deformations of the enveloping algebra of a Lie algebra which is a central extension of sln(Π(Q)) where Π(Q) is the preprojective algebra of Q. When Q is an affine Dynkin quiver of type A, D or E, we can relate them to Γ-deformed double current algebras. We are able to construct functors between d...
متن کامل