带角流形上广义相对论的约化狄拉克结构
The reduced Dirac structure of General Relativity on manifolds with corners
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中文总结 AI 辅助
本文推导四维Palatini-Cartan引力的角泊松结构，利用边界约束代数得到角场空间的预狄拉克结构及约化过程，将约化角理论呈现为类BF理论并导出BF²V形式，为引力的体、边界和角结构提供统一框架基础。
中文摘要 AI 辅助
本文推导了四维Palatini-Cartan引力的角泊松结构。基于边界流形上引力的经典描述，特别是边界约束代数，在角场空间上得到一个预狄拉克结构，同时得到一个约化过程，该过程在角场的约化空间上产生一个极大狄拉克结构，其被确定为泊松双矢量场的图。进一步表明，该泊松结构具有等价的仿射泊松描述，其自然将约化角理论呈现为类BF理论，并导出了BF²V形式。这为Palatini-Cartan引力的体、边界和角结构提供了统一框架的基础。
英文摘要
In this paper, the corner Poisson structure of four-dimensional Palatini-Cartan gravity is derived. Building on the classical description of gravity on manifolds with boundary, specifically on the boundary constraint algebra, a pre-Dirac structure on the space of corner fields is obtained together with a reduction procedure that yields a maximal Dirac structure, identified as the graph of a Poisson bivector field, on the reduced space of corner fields. It is further shown that this Poisson structure admits an equivalent affine Poisson description, which naturally exhibits the reduced corner theory as a $BF$-like theory and leads to a BF$^2$V formulation. This provides the basis for a unified framework for the bulk, boundary, and corner structures of Palatini-Cartan gravity.
