Algebraic solution and thermodynamic properties for the one- and two-dimensional Dirac oscillator with minimal length uncertainty relations

We study the quantum characteristics of the Dirac oscillator within the framework of Heisenberg's generalized uncertainty principle. This principle leads to the appearance of a minimal length of the order of the Planck length. Hidden symmetries are identified to solve the model algebraically. The presence of the minimal length leads to a quadratic dependence of the energy spectrum on the quantum number $n$, implying the hard confinement property of the system. Thermodynamic properties are calculated using the canonical partition function. The latter is well determined by the method based on Epstein's zeta function. The results reveal that the minimal length has a significant effect on the thermodynamic properties.