标题： 广义相对论中的类似聂-杨拓扑不变量 显示英文标题

标题： A Nieh-Yan-like topological invariant in General Relativity

摘要： 在本工作中，我们将引入并证明一个涉及扭率张量的广义相对论中的拓扑不变项，该术语之前从未被展示过。 该术语是对Nieh-Yan四形式的轻微修改，同样源自陈-西蒙斯三形式。 我们分别在正则基和正交基下提供了证明，并表明其积分可简化为一个边界项，在适当条件下该边界项为零。 如同所有拓扑不变对象一样，新项在纯引力中不会影响爱因斯坦场方程，但当物质场与引力场耦合时，扭率张量会出现，其贡献会改变“游戏规则”。 因此，研究这些在原始引力中无关的项如何修改与标准模型场的相互作用具有重要意义。 显示英文摘要

摘要： In the present work we will introduce and prove a topological invariant term in General Relativity involving the torsion tensor that has never been showed before. Such a term is a slight modification of the Nieh-Yan four-form and likewise it stems from a Chern-Simons three-form. We provide the proof in both holonomic and orthogonal basis and show that its integral reduces to a boundary term that vanishes with the right conditions. As all topological invariant objects the new term does not affect the Einstein field equations in pure gravity, but when matter fields couple to the gravitational field, the torsion tensor arises and its contribution changes the "rules of the game". Therefore it is of great importance to study how those pieces irrelevant in bare gravity modify the interaction with fields of the Standard Model.