Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [◯,p] = i(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ∼ SO(2, 1) algebra is satisfied by the operators ± and ẑ.