论文标题
较高的衍生标量调整理论和空间协方差的重力：对应关系
Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
论文作者
论文摘要
我们研究了通常协变的高导数标量探测理论与空间协变重力理论之间的对应关系。构建块是标量场和时空曲率张量以及其前者的通常协变量衍生物，以及空间协变量的几何量以及其后期的空间协变量衍生物。在单个标量的自由度的情况下，它们通过量规固定和恢复程序彼此转换，我们给出了明确的表达方式。根据最高$ d = 4 $的衍生物总数及其与标量调节单元的对应关系，我们对空间协变重力中的所有标量单元进行系统分类。我们讨论了使用空间协变量单元来生成无鬼衍生型标量理论的可能性。我们还可以在不固定任何特定坐标的情况下得出协变量3+1分解，这在执行协方差汉密尔顿分析时将很有用。
We investigate the correspondence between generally covariant higher derivative scalar-tensor theory and spatially covariant gravity theory. The building blocks are the scalar field and spacetime curvature tensor together with their generally covariant derivatives for the former, and the spatially covariant geometric quantities together with their spatially covariant derivatives for the later. In the case of a single scalar degree of freedom, they are transformed to each other by gauge fixing and recovering procedures, of which we give the explicit expressions. We make a systematic classification of all the scalar monomials in the spatially covariant gravity according to the total number of derivatives up to $d=4$, and their correspondence to the scalar-tensor monomials. We discusse the possibility of using spatially covariant monomials to generate ghostfree higher derivative scalar-tensor theories. We also derive the covariant 3+1 decomposition without fixing any specific coordinate, which will be useful when performing a covariant Hamiltonian analysis.
