q-deformed Lie algebras and fractional calculus

TL;DR

This paper explores the connection between fractional calculus and q-deformed Lie algebras, deriving new spectra and transition probabilities that can model nuclear ground states and spectra.

Contribution

It introduces fractional q-deformed Lie algebras, deriving energy spectra and transition probabilities relevant for nuclear structure modeling.

Findings

Derived q-number for fractional harmonic oscillator

Energy spectrum models ground state spectra of nuclei

Calculated B_alpha(E2) values for fractional rotor

Abstract

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.