论文标题
Weyl仪的起源是公制的理论
The origin of Weyl gauging in metric-affine theories
论文作者
论文摘要
在第一部分中，我们从几个不同的观点中讨论了局部规模不变性与公制的自由度之间的相互作用。我们认为，通常认为Weyl对称性的测量是需要规模不变性的自然副产品，这是基于度量的引力理论的对称性，它基于度量和独立的仿射结构自由度。在第二部分中，我们计算了与所有仪表对称性相关的Nöther身份，包括Weyl，Lorentz和Diffemorilisms Invanciances，用于具有自由度的一般行为，并利用了谎言衍生物的量规协方差的概括。我们根据我们如何将自旋连接度自由度视为独立对象或两个Weyl不变术语的总和，找到了两种等效的方法来解决问题。后一种方法基于使用新连接的使用，表示为$ \ hat {\ nabla} $，特别方便，构成了我们的主要结果之一。
In the first part, we discuss the interplay between local scale invariance and metric-affine degrees of freedom from few distinct points of view. We argue, rather generally, that the gauging of Weyl symmetry is a natural byproduct of requiring that scale invariance is a symmetry of a gravitational theory that is based on a metric and on an independent affine structure degrees of freedom. In the second part, we compute the Nöther identities associated with all the gauge symmetries, including Weyl, Lorentz and diffeomorphisms invariances, for general actions with matter degrees of freedom, exploiting a gauge covariant generalization of the Lie derivative. We find two equivalent ways to approach the problem, based on how we regard the spin-connection degrees of freedom, either as an independent object or as the sum of two Weyl invariant terms. The latter approach, which rests upon the use of a new connection, denoted $\hat{\nabla}$, is particularly convenient and constitutes one of our main results.
