标题： 作用量、拓扑项和边界在第一类引力中的研究：综述 显示英文标题

标题： Actions, topological terms and boundaries in first order gravity: A review

摘要： 在本综述中，我们首先考虑四维的一阶引力。特别是，我们关注那些基本变量为一个四维标架$e_a^I$和一个 SO(3,1) 连接${\omega_{aI}}^J$的形式化方法。我们研究与微分同胚不变性相容的最一般的作用原理。这意味着，除了标准的爱因斯坦-希爾伯特-帕拉廷项外，还考虑其他不会改变运动方程或具有拓扑性质的项。拥有一个明确的作用原理有时需要添加额外的边界项，其具体形式可能取决于当前的边界条件。在本工作中，我们考虑包含在无穷远处有边界的空间时间，满足渐近平坦的边界条件和/或满足孤立视界边界条件的内部边界。我们专注于协变哈密顿形式，其中相空间$\Gamma$由运动方程的解给出。对于作用量中可能的每个项，我们考虑作用量的适定性、有限性、对辛结构的贡献以及哈密顿和诺特定荷。对于所选的边界条件，标准边界项保证理论的适定性。此外，边界项和拓扑项不对辛结构以及哈密顿守恒荷产生贡献。另一方面，诺特定荷确实依赖于这些附加项。本文的目的是提供一个全面且自洽的处理方式，因此风格有些教学性质。此外，在此过程中，我们指出并澄清了一些文献中尚未明确理解的问题。 显示英文摘要

摘要： In this review we consider first order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad $e_a^I$ and a SO(3,1) connection ${\omega_{aI}}^J$. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein-Hilbert-Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space $\Gamma$ is given by solutions to the equations of motion. For each of the possible terms contributing to the action we consider the well posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way we point out and clarify some issues that have not been clearly understood in the literature.