Exact Green's function for 2D dirac oscillator in constant magnetic field within curved snyder space, and its thermal properties

Following the path integral approach, and in the context of curved Snyder space, we formulate the Green function for a (1+1)-dimensional Dirac oscillator system subject to a homogeneous magnetic field. Using the radial coordinates transformation the Green function and the electron propagator are calculated. Consequently, the exact bound states and their corresponding spectral energies are extracted. Our analysis has revealed that, under specific conditions when m omega over bar -> m omega c/2 and c -> V F , the behavior of the Dirac oscillator system in the presence of a uniform magnetic field within the SdS algebra closely resembles the dynamics of the monolayer graphene problem in the same algebraic framework. At high temperatures, the thermodynamic properties of the electron gas in the four cases of deformation parameters were extracted. The effect of the deformation parameters on these properties are tested, and also the limit cases for small parameters were inferred.