We study the effects of Snyder–de Sitter commutation relations on relativistic bosons by solving analytically in the momentum space representation the Klein–Gordon oscillator in arbitrary dimensions. The exact bound state spectrum and the corresponding momentum space wave functions are obtained using Gegenbauer polynomials in the one-dimensional space and Jacobi polynomials in the D-dimensional case. Finally, we study the thermodynamic properties of the system in the high-temperature regime where we found that the corrections increase the free energy but decrease the energy, the entropy, and the specific heat that is no longer constant. This work extends the part concerning the Klein–Gordon oscillator for the Snyder–de Sitter case studied in two-dimensional space by Falek et al. [J. Math. Phys. 60, 013505 (2019)].

中文翻译：

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D 维 Klein-Gordon 振荡器与 Snyder-de Sitter 代数的精确解

我们通过在任意维度的 Klein-Gordon 振荡器的动量空间表示中解析求解，研究 Snyder-de Sitter 对易关系对相对论玻色子的影响。使用一维空间中的 Gegenbauer 多项式和 D 维情况下的雅可比多项式获得精确的束缚态谱和相应的动量空间波函数。最后，我们研究了系统在高温状态下的热力学性质，我们发现修正增加了自由能，但降低了能量、熵和不再恒定的比热。这项工作扩展了 Falek 等人在二维空间中研究的 Snyder-de Sitter 案例中关于 Klein-Gordon 振荡器的部分。[J. 数学。物理。60, 013505 (2019)]。