标题： 广义引力 显示英文标题

标题： Extended Gravity

摘要： 我们将展示Palatini-$f(\calR)$理论与Brans-Dicke (BD)理论在作用量原理层面的等价性，在通用维度和通用物质耦合情况下。我们通过引入与Palatini-$f(\calR)$理论相关的Helmholtz拉格朗日量，然后进行框架变换以恢复爱因斯坦框架和Brans-Dicke框架。这澄清了不同表述之间的关系以及不同框架之间的变换。此外，它为Brans-Dicke理论定义了一个表述{\it 拉 Palatini}，该表述与度规BD（不同于标准度规BD理论的Palatini表述，这些表述是{\it 不是}动态等价的）。最后，我们讨论了引力扩展理论的解释和前景。 显示英文摘要

摘要： We shall show equivalence between Palatini-$f(\calR)$ theories and Brans-Dicke (BD) theories at the level of action principles in generic dimension with generic matter coupling. We do that by introducing the Helmholtz Lagrangian associated to Palatini-$f(\calR)$ theory and then performing frame transformations in order to recover Einstein frame and Brans-Dicke frame. This clarifies the relation among different formulations and the transformations among different frames. Additionally, it defines a formulation {\it a l\'a Palatini} for the Brans-Dicke theory which is dynamically equivalent to metric BD (unlike the standard Palatini-formulation of metric BD theory which are {\it not} dynamically equivalent). In conclusion we discuss interpretation of extended theories of gravitation and perspectives.