In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties that had been encountered in the earlier treatment. In this approach, gravity is formulated entirely in terms of Dirac observables without constraints, opening attractive new possibilities for quantization. In this paper we discuss the Poisson algebra of the resulting Dirac observables, associated with the intrinsic components of the Riemann tensor. This provides an explicit realization of the non-local algebra of observables for gravity that several authors have conjectured.

中文翻译：

---

可观测量的引力 2：基本可观测量的代数

在之前的一篇论文中，我们展示了如何使用环群技术来制定 Mandelstam 在 1960 年代提出的重力环方法。这些技术可以克服在早期治疗中遇到的一些困难。在这种方法中，引力完全根据狄拉克可观察量进行表述，没有限制，为量化开辟了有吸引力的新可能性。在本文中，我们讨论所得狄拉克可观测量的泊松代数，与黎曼张量的内在分量相关。这提供了几个作者推测的重力可观测量的非局部代数的明确实现。