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arXiv 1802.02661gr-qchep-th
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引力的可观测性

Gravitation in terms of observables

Rodolfo Gambini, Jorge Pullin

摘要:

在20世纪60年代,Mandeltek提出了一种基于回路的规范理论和引力的新方法。规范理论的程序是由Gambini和Trias在20世纪80年代完成的。规范理论可以理解为特定群的表示:环群。同样的形式主义在当时还不能应用于引力的情形。在这里,我们想提出一个扩展到重力的情况。由此产生的理论被描述为环路和开放路径,并可以提供一个新的量子表示的重力不同于环量子引力或弦论中使用的基础。在它里面,时空点是只具有准经典状态的涌现实体。这个公式可以完全用狄拉克观测量给出,狄拉克观测量形成了一套完整的规范不变函数,完全定义了时空的黎曼几何。在量子水平上,该公式将导致没有任何约束的减少的相空间量化。

英文摘要:

In the 1960's, Mandelstam proposed a new approach to gauge theories and gravity based on loops. The program for gauge theories was completed for Yang--Mills theories by Gambini and Trias in the 1980's. Gauge theories could be understood as representations of certain group: the group of loops. The same formalism could not be implemented at that time for the gravitational case. Here we would like to propose an extension to the case of gravity. The resulting theory is described in terms of loops and open paths and can provide the underpinning for a new quantum representation for gravity distinct from the one used in loop quantum gravity or string theory. In it, space-time points are emergent entities that would only have quasi-classical status. The formulation may be given entirely in terms of Dirac observables that form a complete set of gauge invariant functions that completely define the Riemannian geometry of the spacetime. At the quantum level this formulation will lead to a reduced phase space quantization free of any constraints.

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