论文标题
阿贝尔对称性和palatini变化
Abelian symmetry and the Palatini variation
论文作者
论文摘要
爱因斯坦 - 希尔伯特作用中的度量和连接的独立变化，称为palatini变化，通常被视为等同于通常的一般相对性的表述，其中只有度量的变化。但是，当允许使用Abelian对称性进行连接时，Palatini变化会导致可集成的Weyl几何形状，而不是Riemannian。我们使用两个可能的度量/连接对得出了这一结果：（1）指标和一般坐标连接以及（2）PoincarèGauge理论的焊料形式和局部Lorentz自旋连接。两者都得出相同的结论。最后，我们将工作与文献中的其他疗法联系起来。
Independent variation of the metric and connection in the Einstein-Hilbert action, called the Palatini variation, is generally taken to be equivalent to the usual formulation of general relativity in which only the metric is varied. However, when an abelian symmetry is allowed for the connection, the Palatini variation leads to an integrable Weyl geometry, not Riemannian. We derive this result using two possible metric/connection pairs: (1) the metric and general coordinate connection and (2) the solder form and local Lorentz spin connection of Poincarè gauge theory. Both lead to the same conclusion. Finally, we relate our work to other treatments in the literature.
