Abstract
The Dirac and Klein-Gordon oscillators on anti-de Sitter space were considered in a space with deformed commutation relations. Anti-de Sitter commutation relations give rise to the appearance of minimal uncertainty in the momentum. Using the position space representation, we determine the energy eigenvalues and the eigenfunctions for both cases. The wave functions can be given in terms of Gegenbauer polynomials. The high-temperature thermodynamic properties of the relativistic harmonic oscillators are then analyzed.
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