标题： 引力的弱场展开和图形表示 显示英文标题

标题： Weak Field Expansion of Gravity and Graphical Representation

摘要： 我们引入了一个全局SO(n)张量$\pl_\m\pl_\n h_\ab$的图形表示，这通常出现在平坦空间周围引力微扰方法中：$g_\mn=\del_\mn+h_\mn$。我们系统地构造了全局SO(n)不变量。通过取$\pl\pl h$-和$ (\pl\pl h)^2$-不变量的例子，展示了这些不变量的独立性和完备性。它们被以图形方式分类。给出了表征所有独立不变量（或图）的指标。我们将结果应用于维度为$(Mass)^4$的一般不变量以及四维引力中的高斯-博内恒等式。 显示英文摘要

摘要： We introduce a graphical representation for a global SO(n) tensor $\pl_\m\pl_\n h_\ab$, which generally appears in the perturbative approach of gravity around the flat space: $g_\mn=\del_\mn+h_\mn$. We systematically construct global SO(n) invariants. Independence and completeness of those invariants are shown by taking examples of $\pl\pl h$-, and $ (\pl\pl h)^2$- invariants. They are classified graphically. Indices which characterize all independent invariants (or graphs) are given. We apply the results to general invariants with dimension $(Mass)^4$ and the Gauss-Bonnet identity in 4-dim gravity.