One-dimensional Dirac oscillator with generalized Snyder model in a thermal bath

Following the path integral approach and within in the context of nonrelativistic Snyder–de Sitter algebra, we formulate the Green function for Dirac oscillator particle in ([Formula: see text]) space-time dimension. Using the momentum space representation [Formula: see text], we determine the energy eigenvalues and the eigenfunctions, where the wave functions can be given in terms of Gegenbauer polynomials. In addition, the high-temperature thermodynamic properties of the relativistic harmonic oscillators are analyzed, which we found that the heat capacity is not equal two times greater than the heat capacity of the one-dimensional harmonic oscillator for higher temperatures in SdS model. The special cases are found and discussed.