Title: Towards general relativity through parametrized theories Show Chinese title

Title: 通过参数化理论走向广义相对论

Abstract: Boundaries, GNH, and parametrized theories. It takes three to tango. This is the motto of my doctoral thesis and the common thread of it. The thesis is structured as follows: after some acknowledgments and a brief introduction, chapter one is devoted to establishing the mathematical background necessary for the rest of the thesis (with special emphasis in the space of embeddings and the Fock construction). Chapter two is based on our papers arXiv:1701.00735, arXiv:1611.09603, and arXiv:1501.05114. We study carefully a system consisting of a string with two masses attached to the ends and try to establish if we can identify degrees of freedom at the boundary both classically and quantically (spoiler alert: it is not possible). The next chapter is a brief introduction to the parametrized theories with the simple example of the parametrized classical mechanics. The 4th chapter deals with the parametrized electromagnetism with boundaries, a generalization of our paper arXiv:1511.00826. The following chapter focuses on the parametrized scalar field with boundaries (see arXiv:1507.05438). The 6th chapter deals with the parametrized Maxwell-Chern-Simons and Chern-Simons theories with boundaries. Chapter seven delves into the theory of general relativity using the GNH algorithm, showing that the Hamiltonian formulation (ADM) can be obtained in a more direct and simple way. The same study is performed over the unimodular gravity. In the last chapter we gather the conclusions and some hints about the future work. Finally, an appendix is included with some additional mathematical topics as well as explicit computations. Show Chinese abstract

Abstract: 边界、GNH和参数化理论。 三人共舞。 这是我的博士论文的座右铭，也是贯穿全文的主线。 论文的结构如下：在一些致谢和简短的引言之后，第一章致力于建立论文其余部分所需的数学基础（特别强调嵌入空间和福克构造）。 第二章基于我们的论文arXiv:1701.00735、arXiv:1611.09603和arXiv:1501.05114。 我们仔细研究了一个由两个质量连接在两端的弦系统，并试图确定是否可以在经典和量子情况下识别边界上的自由度（剧透警告：这是不可能的）。 下一章是对参数化理论的简要介绍，以参数化经典力学的简单例子为例。 第四章涉及带有边界的参数化电磁学，这是我们论文arXiv:1511.00826的推广。 接下来的一章专注于带有边界的参数化标量场（参见arXiv:1507.05438）。 第六章涉及带有边界的参数化麦克斯韦-陈-西蒙斯和陈-西蒙斯理论。 第七章深入研究了广义相对论理论，使用GNH算法，表明哈密顿形式（ADM）可以通过更直接和简单的方式获得。 同样的研究也应用于单模引力。 在最后一章中，我们总结了结论以及对未来工作的建议。 最后，附录中包含了一些额外的数学主题以及显式的计算。