We review on further new developments of Generalized Uncertainty Principle (GUP) and implications for the cosmological vacuum energy. First, we introduce basic aspects of GUP as well as several possible different and viable formulation of it. Second, we move on discussing two recent new types of higher D-dimensional nonperturbative GUP models; which we dub D-Type-I and D-Type-II GUPs. The D-Type-I and D-Type-II GUPs are both related to the existence of a critical conspiracy between a minimal uncertainty length and a maximal observable momentum. Finally, we show direct implications of D-Type-I and D-Type-II on the cosmological vacuum energy obtained in quantum mechanical systems such as the typical quantum harmonic oscillator. Such a computation goes through investigations of the density of states for D-dimensional coordinate systems in the momentum space. We will also comment on several possible connections with fundamental issues of quantum gravity such as black hole physics and gravitational radiative aspects.

中文翻译：

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非微扰 GUP 模型的各个方面

我们回顾了广义不确定性原理 (GUP) 的进一步新发展以及对宇宙真空能量的影响。首先，我们介绍 GUP 的基本方面以及它的几种可能的不同和可行的表述。其次，我们继续讨论最近两种新型的高 D 维非微扰 GUP 模型；我们将其称为 D-Type-I 和 D-Type-II GUP。D-Type-I 和 D-Type-II GUP 都与最小不确定性长度和最大可观察动量之间的关键阴谋的存在有关。最后，我们展示了 D-Type-I 和 D-Type-II 对在量子力学系统（例如典型的量子谐振子）中获得的宇宙真空能量的直接影响。这种计算通过对动量空间中 D 维坐标系的状态密度的研究。我们还将评论与量子引力的基本问题（例如黑洞物理学和引力辐射方面）的几种可能联系。