q-deformed Lie algebras and fractional calculus

Details q-deformed Lie algebras and fractional calculus q-deformed Lie algebras and fractional calculus

2007-11-23

arxiv.org/abs/0711.3701v1

Physica A 389 (2010) 4613--4622

Physics

General Physics

8 pages, 3 figures

Scientific paper

10.1016/j.physa.2010.07.004

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 $B_\alpha(E2)$ values for the fractional q-deformed symmetric rotor are calculated.

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