论文标题
2+1维度的大量重力理论
Theories of Massive Gravity in 2+1 Dimensions
论文作者
论文摘要
本论文致力于研究大量重力理论。介绍了较高的自旋量规理论的配方，以及Chern-Simons（CS）（例如较高自旋场的术语）。通过这种设置，讨论了在任意维度中描述较高自旋的无质量/大型领域的理论的一般特征。在2+1个维度中，存在多种质量生成机制的存在，即基于公制的质量和拓扑质量，为仪表玻色子提供了获得混合质量的可能性。这种情况首先是在光子理论中引入的，其中Proca质量项和CS质量术语同时存在。通过Stückelberg形式主义进一步分析了该理论中发生的大规模混合。在这些结果的动机中，研究了一种大量重力理论，其中重力从Fierz-Pauli质量项和CS质量项都得到了研究。该理论允许3种传播大量的重力模式，它们的质量经历了相当大的混合。通过Stückelberg分析，将这种质量混合显式。重力理论是对一般相对论理论的非平凡概括。该理论提供了详细研究的一致的非线性重力理论。在本论文中，重力理论在2+1尺寸上扩展到拓扑上质量的双灵重力理论（TMBG）。在TMBG的理论中，由两个指标的相互作用产生的质量混合及其相应的CS项发生在非线性阶段本身。对于本文研究的TMBG版本，线性化理论表明，有3种巨大的重力模式，与前面发现的相同3个模式相对应。最后，计算了从大量光子（从CS和Proca机制中获取质量）对重力传播器的量子环校正。
This thesis is dedicated to the study of theories of massive gravity. The formulation of higher spin gauge field theories, along with a Chern-Simons (CS) like term for fields of higher spins is presented. Through this setup, general features of theories describing massless/massive fields of higher spin in arbitrary dimensions is discussed. In 2+1 dimensions, the existence of multiple mass-generating mechanisms i.e. metric-based masses and topological masses, offers the possibility for gauge bosons to acquire mixed masses. This scenario is first introduced in a theory of photons where both Proca mass term and CS mass term is simultaneously present. The mass-mixing which occurs in this theory is further analysed through the Stückelberg formalism. Motivated by these results, a theory of massive gravity where gravitons obtain masses from both Fierz-Pauli mass term and CS mass term is studied. This theory allows for 3 propagating massive graviton modes, and their masses have undergone considerable mixing. This mass-mixing is made explicit through a Stückelberg analysis. The bimetric theory of gravity is a non-trivial generalization of the theory of General Relativity. This theory provides a consistent non-linear theory of massive gravity which is studied in detail. In this thesis, the bimetric theory of gravity is extended in 2+1 dimensiosn to the theory of Topologically Massive Bimetric Gravity (TMBG). In the theory of TMBG, the mass-mixing which arises from the interaction of the two metrics and their corresponding CS terms occurs at the nonlinear stage itself. For the version of TMBG studied in this thesis, the linearized theory shows that there are 3 massive graviton modes, which corresponds to the same 3 modes found earlier. Finally, quantum loop corrections to the graviton propagator from massive photons (which acquire mass from both CS and Proca mechanism) is calculated.
