近日，意大利斯科拉国际博览中心（SISSA）的Eyoab Bahiru及其研究团队取得一项新进展。经过不懈努力，他们对量子引力中的代数及其协变表示进行研究。相关研究成果已于2024年7月2日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队研究了引力和非引力理论中算子代数的物理动机性表示，称为代数的协变表示。这是一种表示，其中算子代数的对称性在希尔伯特空间上被统一地实现。

研究人员强调这种表示与代数的叉积非常相似。事实上，作为协方差代数的一个例子(有时也等同于)，一个代数的叉乘与该代数的协变表示是一一对应的。这将反过来说明在量子引力的背景下交叉积代数是什么。

附：英文原文

Title: Algebras and their covariant representations in quantum gravity

Author: Bahiru, Eyoab

Issue&Volume: 2024-07-02

Abstract: We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator algebra are implemented unitarily on the Hilbert space. We emphasize the very close similarity of this representation to the crossed product of an algebra. In fact, as an example of (and sometimes identified with) a covariance algebra, the crossed product of an algebra is in one to one correspondence with the covariant representation of the algebra. This will in turn illuminate physically what the crossed product algebra is in the context of quantum gravity.

DOI: 10.1007/JHEP07(2024)015

Source: https://link.springer.com/article/10.1007/JHEP07(2024)015