arXiv 2203.086922022-03hep-thgr-qc

度量仿射理论中Weyl规范的起源

The origin of Weyl gauging in metric-affine theories

Dario Sauro, Omar Zanusso

备注：: 37 pages
发表信息：: Class.Quant.Grav. 39 (2022) 18, 185001
DOI：: 10.1088/1361-6382/ac82a2

摘要：

在第一部分中，我们从几个不同的角度讨论了局部尺度不变性和度量仿射自由度之间的相互作用。我们认为，而一般来说，外尔对称性的测量是一个自然的副产品，要求标度不变性是一个对称的引力理论，是基于一个度量和一个独立的仿射结构自由度。在第二部分中，我们计算与所有的规范对称性，包括外尔，洛伦兹和同态不变性，为物质自由度的一般行动，利用规范协变推广的李导数的Nöther身份。我们找到两种等价的方法来解决这个问题，根据我们如何看待自旋连接自由度，无论是作为一个独立的对象或作为两个外尔不变项的总和。后一种方法，它依赖于使用一个新的连接，表示为$\hat{\nabla}$，是特别方便，并构成我们的主要结果之一。

英文摘要：

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.

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英文摘要：

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