标题： 模糊引力：协变非对易空间上的四维引力与内部相互作用的统一 显示英文标题

标题： Fuzzy Gravity: Four-Dimensional Gravity on a Covariant Noncommutative Space and Unification with Internal Interactions

摘要： 在本工作中，我们对协变非对易空间进行了扩展描述，该空间容纳了之前构建的模糊引力模型。 它是基于一个历史教训，即使用包含连续空间所有对称性生成元的更大代数有助于构造模糊协变非对易空间。 具体而言，对称性群的进一步扩大不仅导致了协变非对易空间的构造，还提出了应在这样的空间上规范化的群，以构建模糊引力理论。 因此，我们得到了两种模糊引力模型，一种在德西特空间，另一种在反德西特空间，这取决于对称性群的扩展，并讨论了它们的自发对称性破缺，从而得到非对易$SO(1,3)$引力的模糊版本。 此外，我们首次讨论了如何在模糊引力中引入费米子，更重要的是如何将构建的非对易-模糊引力与基于$SO(10)$或$SU(5)$的内部相互作用统一起来，作为大统一理论。 显示英文摘要

摘要： In the present work we present an extended description of the covariant noncommutative space, which accommodates the Fuzzy Gravity model constructed previously. It is based on the historical lesson that the use of larger algebras containing all generators of the isometry of the continuous one helped in formulating a fuzzy covariant noncommutative space. Specifically a further enlargement of the isometry group leads us, in addition to the construction of the covariant noncommutative space, also to the suggestion of the group that should be gauged on such a space in order to construct a Fuzzy Gravity theory. As a result, we obtain two Fuzzy Gravity models, one in de Sitter and one in anti-de Sitter space, depending on the extension of the isometry group, and we discuss their spontaneous symmetry breaking leading to fuzzy versions of the noncommutative $SO(1,3)$ gravity. In addition we discuss for the first time how to introduce fermions in the fuzzy gravity and even more importantly how to unify the constructed noncommutative-fuzzy gravity with internal interactions based on $SO(10)$ or $SU(5)$ as grand unified theories.