关于共形群度量的新观点
Fresh perspective on gauging the conformal group
摘要：
我们考虑构造在局部共形变换下不变的引力规范理论。我们首先澄清的几何性质的全球共形变换，在他们的无穷小和有限的形式，和后果的全球共形不变性的场论，重新考虑现有的方法，测量的共形群，即辅助共形规范理论和双共形规范理论，这两个都不是普遍接受的完整的解决方案。然后，我们证明，任何物质场属于一个不可约表示的洛伦兹群，最近提出的扩展外尔规范理论（eWGT）可以被认为是一种替代方法，用于规范的共形群，因为eWGT是不变的全套下的局部共形变换，包括反演，以及拥有守恒定律，该守恒定律提供了具有全局共形不变性的场论所满足的那些守恒定律的自然局部概括，并且还具有对应于全局共形变换的“无规范”极限。相比之下，虽然标准外尔规范理论也具有第一个性质，但它不具有另外两个性质，因此不能被认为是共形群的有效规范理论。
英文摘要：
We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and the consequences of global conformal invariance for field theories, before reconsidering existing approaches for gauging the conformal group, namely auxiliary conformal gauge theory and biconformal gauge theory, neither of which is generally accepted as a complete solution. We then demonstrate that, provided any matter fields belong to an irreducible representation of the Lorentz group, the recently proposed extended Weyl gauge theory (eWGT) may be considered as an alternative method for gauging the conformal group, since eWGT is invariant under the full set of local conformal transformations, including inversions, as well as possessing conservation laws that provide a natural local generalisation of those satisfied by field theories with global conformal invariance, and also having an `ungauged' limit that corresponds to global conformal transformations. By contrast, although standard Weyl gauge theory also enjoys the first of these properties, it does not share the other two, and so cannot be considered a valid gauge theory of the conformal group.
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