标题： 非线性场论的新补充条件：广义相对论 显示英文标题

标题： New Supplementary Conditions for a Non-Linear Field Theory: General Relativity

摘要： 广义相对论的爱因斯坦理论提供了经典场论的一个特殊例子，该理论由非线性偏微分方程支配。 文献中也考虑了一些补充条件（更常被称为规范条件）。 在本文中，从de Donder规范出发，该规范不是共形不变的，但它是Lorenz规范的引力对应物，我们通过向量丛上的几何结构，考虑了广义相对论中一个新的规范族，该规范涉及度规扰动的五阶协变导数。 介绍了作者最近结果的综述：对时空上对称二阶张量场向量丛上的度规一般形式的限制；在平坦欧几里得空间附近的线性化理论情况下，此类规范的可接受性；通过求解积分方程，推广到合适的曲黎曼背景。 最后，讨论了其在欧几里得量子引力中的应用。 显示英文摘要

摘要： The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also been considered in the literature. In the present paper, starting from the de Donder gauge, which is not conformally invariant but is the gravitational counterpart of the Lorenz gauge, we consider, led by geometric structures on vector bundles, a new family of gauges in general relativity, which involve fifth-order covariant derivatives of metric perturbations. A review of recent results by the authors is presented: restrictions on the general form of the metric on the vector bundle of symmetric rank-two tensor fields over space-time; admissibility of such gauges in the case of linearized theory about flat Euclidean space; generalization to a suitable class of curved Riemannian backgrounds, by solving an integral equation. Eventually, the applications to Euclidean quantum gravity are discussed.