标题： 引力的规范理论：非线性框架 显示英文标题

标题： Gauge theories of gravity: the nonlinear framework

摘要： 非线性时空群实现被介绍为一种通用的数学工具，为引力的规范理论的不同表述提供了共同基础。 我们特别将非线性实现应用于庞加莱群和仿射群，以分别发展庞加莱规范理论（PGT）和度规-仿射引力（MAG）。 关于PGT，开发了两种替代的庞加莱群非线性处理方法，其中一种适用于处理拉格朗日形式，另一种适用于处理同一规范理论的哈密顿形式。 我们认为我们的PGT哈密顿方法与阿什特卡（Ashtekar）的引力方法密切相关。 另一方面，对MAG的简要概述阐明了度规-仿射度规张量作为戈德斯通场的作用。 事实上，所有引力量——度规以及余标架和联络——在非线性框架中都被显示具有简单的规范理论解释。 显示英文摘要

摘要： Nonlinear realizations of spacetime groups are presented as a versatile mathematical tool providing a common foundation for quite different formulations of gauge theories of gravity. We apply nonlinear realizations in particular to both the Poincar\'e and the affine group in order to develop Poincar\'e gauge theory (PGT) and metric-affine gravity (MAG) respectively. Regarding PGT, two alternative nonlinear treatments of the Poincar\'e group are developed, one of them being suitable to deal with the Lagrangian and the other one with the Hamiltonian version of the same gauge theory. We argue that our Hamiltonian approach to PGT is closely related to Ashtekar's approach to gravity. On the other hand, a brief survey on MAG clarifies the role played by the metric--affine metric tensor as a Goldsone field. All gravitational quantities in fact --the metric as much as the coframes and connections-- are shown to acquire a simple gauge--theoretical interpretation in the nonlinear framework.