Common aspects of q-deformed Lie algebras and fractional calculus

Abstract

Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the first time allows a smooth transition between different Lie algebras. For the fractional harmonic oscillator, the corresponding fractional q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool to describe e.g. 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 $B_{\alpha }(E2)$ values for the fractional q-deformed symmetric rotor are calculated. A first interpretation of half integer representations of the fractional rotation group is given in terms of a description of $K=1/2^{-}$ band spectra of odd-even nuclei.

14 pages, 4 figures, accepted for publication Physica A

References in corpus (7)

• Dynamics with Low-Level Fractionality
• Gauge invariance in fractional field theories
• The fractional symmetric rigid rotor
• Fractional dynamic symmetries and the ground state properties of nuclei
• Repulsive Casimir Force from Fractional Neumann Boundary Conditions
• Remarcs on the shape transition from spherical to deformed gamma unstable nuclei
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Cited by in corpus (4)

• On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric
• Infrared spectroscopy of diatomic molecules - a fractional calculus approach
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Static hyperpolarizability of space-fractional quantum systems