论文标题
爱因斯坦重力作为保形群的尺度理论
Einstein gravity as a gauge theory for the conformal group
论文作者
论文摘要
维度的一般相对性$ n = p+q $可以作为共形组$ so（p+1，q+1）$的规格理论配方，以及一个额外的字段，将结构组降低到Poincarégroup $ iso（p，q）$。在本文中，我们提出了一个新的爱因斯坦几何学变化原理，该原理意识到了这一事实。重要的是，与文献中先前的治疗相反，我们的作用功能给出了一阶场方程，并且不需要对量规场（例如扭转且繁琐）的补充约束。 我们的方法基于保形拖拉机几何形状的“一阶公式”。因此，它提供了爱因斯坦方程的拖拉机版本的直接变异推导。为了实现这一目标，我们从尺度理论的角度回顾了拖拉机几何形状的标准理论，从抽象的主捆绑包中定义了先验拖拉机束，并通过动态焊接形式提供标准的保形拖拉机束。这也可以看作是对所谓的Cartan-Palatini公式的概括，其中“内部”正交组$ SO（P，Q）$将其扩展到适当的抛物线子组$ P \ subset SO（P+1，Q+1）$的共形组。
General Relativity in dimension $n = p + q$ can be formulated as a gauge theory for the conformal group $SO(p+1,q+1)$, along with an additional field reducing the structure group down to the Poincaré group $ISO(p,q)$. In this paper, we propose a new variational principle for Einstein geometry which realizes this fact. Importantly, as opposed to previous treatments in the literature, our action functional gives first order field equations and does not require supplementary constraints on gauge fields, such as torsion-freeness. Our approach is based on the "first order formulation" of conformal tractor geometry. Accordingly, it provides a straightforward variational derivation of the tractor version of the Einstein equation. To achieve this, we review the standard theory of tractor geometry with a gauge theory perspective, defining the tractor bundle a priori in terms of an abstract principal bundle and providing an identification with the standard conformal tractor bundle via a dynamical soldering form. This can also be seen as a generalization of the so called Cartan-Palatini formulation of General Relativity in which the "internal" orthogonal group $SO(p,q)$ is extended to an appropriate parabolic subgroup $P\subset SO(p+1,q+1)$ of the conformal group.
