标题： 对经典引力非交换描述的评论 显示英文标题

标题： Comments on the Non-Commutative Description of Classical Gravity

摘要： 我们发现了一族单参数的拉格朗日描述，用于以四维标架表示的经典广义相对论，这些四维标架不是c数。相反，它们服从奇特的对易关系。这些非对易性质在理论的度规部分中消失，在那里克里斯托费尔符号和黎曼张量是普通的对易对象，并且它们由度规张量的通常表达式给出。尽管度规张量不是c数，但我们认为在这个理论中可以进行的所有测量都与c数相关，因此我们的单参数变形规范理论的共同不变部分（对于零扭率的情况）在物理上等价于爱因斯坦的广义相对论。 显示英文摘要

摘要： We find a one-parameter family of Lagrangian descriptions for classical general relativity in terms of tetrads which are not c-numbers. Rather, they obey exotic commutation relations. These noncommutative properties drop out in the metric sector of the theory, where the Christoffel symbols and the Riemann tensor are ordinary commuting objects and they are given by the usual expression in terms of the metric tensor. Although the metric tensor is not a c-number, we argue that all measurements one can make in this theory are associated with c-numbers, and thus that the common invariant sector of our one--parameter family of deformed gauge theories (for the case of zero torsion) is physically equivalent to Einstein's general relativity.