arXiv 1202.61832012-02-28gr-qchep-th

引力的规范理论方法

A Gauge Theoretic Approach to Gravity

Kirill Krasnov

备注：: 40 pages; invited review to appear in Proceedings of the Royal Society A
DOI：: 10.1098/rspa.2011.0638

摘要：

爱因斯坦的广义相对论（GR）是时空度规的动力学理论。我们描述了一种方法，其中GR成为SU（2）规范理论。我们开始在线性化的水平，并显示如何规范理论的拉格朗日非相互作用的无质量自旋两个粒子（引力子）需要一个更简单和紧凑的形式比在标准的度量描述。此外，与GR情形相反，规范理论拉格朗日量是凸的。然后，我们继续制定完整的非线性理论。与基于度量的GR的等价性仅在场方程的解的水平上，即在壳层上成立。规范理论的方法也清楚地表明，GR不是唯一的相互作用理论的无质量自旋两个粒子，尽管GR唯一性定理可在度规描述。因此，存在一个无限参数类的引力理论，它们都只描述引力子的两个传播极化。我们描述了如何可以耦合到重力在这个公式，特别是，如何出现的重力和杨米尔斯作为部门的一般非同态不变的规范理论。最后，我们概述了一个可能的情况下，紫外线完成的量子引力在这种方法。

英文摘要：

Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full non-linear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an inifnite-parameter class of gravity theories all describing just two propagating polarisations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang-Mills arise as sectors of a general diffeomorphism invariant gauge theory. We finish by outlining a possible scenario of the UV completion of quantum gravity within this approach.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文