标题： Weyl群的规范理论及其作为Weyl二次引力的解释 显示英文标题

标题： The Gauge Theory of Weyl Group and its Interpretation as Weyl Quadratic Gravity

摘要： 在本文中，我们对Weyl二次引力作为Weyl群的规范理论进行了详尽的描述。先前发现的（矢量）扭力/非度规性等价性被证明是内置的，因为它对应于Weyl群生成元的重新定义。我们提出了一个扭力/非度规性对偶性的推广，该推广除了矢量外，还包括一个具有两个反对称指标且反对称部分为零的无迹三阶张量。给出了在最小耦合物质场情况下的此关系讨论。我们进一步指出，Rarita-Schwinger场可以最小地耦合到扭力的所有分量和非度规性的某些分量。同时，我们对庞加莱群和共形群进行了相同的规范构造。我们表明，尽管Weyl群是共形群的一个子群，但后者规范理论实际上是Weyl二次引力的一个特例。 显示英文摘要

摘要： In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a redefinition of the generators of the Weyl group. We present a generalisation of the torsion/non-metricity duality which includes, aside from the vector, also a traceless 3-tensor with two antisymmetric indices and vanishing skew symmetric part. A discussion of this relation in the case of minimally coupled matter fields is given. We further point out that a Rarita-Schwinger field can couple minimally to all the components of torsion and some components of non-metricity. Alongside we present the same gauge construction for the Poincar\'e and conformal groups. We show that even though the Weyl group is a subgroup of the conformal group, the gauge theory of the latter is actually only a special case of Weyl quadratic gravity.