We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order. From the point of view of the effective field theory, the third or even higher order covariant derivatives of the scalar field are of the same importance as the higher curvature terms, and thus should be taken into account. Moreover, the higher curvature terms and the higher order derivatives of the scalar field are complementary to each other, of which novel ghostfree combinations may exist. We make a systematic classification of all the possible monomials, according to the numbers of the Riemann tensor and the higher derivatives of the scalar field in each monomial. A complete basis of monomials at each order is derived, of which the linear combinations may yield novel ghostfree Lagrangians. We also develop diagrammatic representations for the monomials, which may help to simplify the analysis.

我们对由Riemann曲率张量构建的标量单项式进行完全分类，直到二次方为止，对标量场的协变导数进行分类，直至三阶。从有效场论的观点来看，标量场的三阶甚至更高阶协变导数与高曲率项具有相同的重要性，因此应予以考虑。此外，标量场的较高曲率项和较高阶导数彼此互补，其中可能存在新颖的无鬼影组合。我们根据每个单项式中的黎曼张量和标量场的高阶导数对所有可能的单项式进行系统分类。得出每个顺序的单项式的完整基础，其中的线性组合可以产生新颖的无鬼拉格朗日数。我们还开发了单项式的图解表示，这可能有助于简化分析。