The generalization of the Heisenberg uncertainty principle has been proposed by different theories of quantum gravity. This deformation affects the quantum phenomena. In this work, we consider the modification of the linear momentum based on the non-locality, and by using it, we calculate the deformed commutation relation between position and momentum. Then, we show how this generalization of the commutation relation affects the angular momentum algebra and its spectrum.

中文翻译：

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GUP及其在角动量代数中的应用

不同的量子引力理论提出了海森堡测不准原理的推广。这种变形会影响量子现象。在这项工作中，我们考虑了基于非定域性的线性动量的修正，并通过使用它，我们计算了位置和动量之间的变形对向关系。然后，我们展示了对换关系的这种推广如何影响角动量代数及其频谱。