The simplest form of the $\kappa$ and ${\kappa }^2$ order graviton self-interaction Lagrangian density in the weak field approximation

Abstract

We derive the simplest form of the $\kappa ({\kappa }^2)$ order graviton self-interaction Lagrangian density $\text{lag}1(\text{lag}2)$ in the weak field approximation. With the divergenceless condition, de Donder gauge and some combinatoric techniques, we derive the mathematically independent basis expressions for $\text{lag}1(\text{lag}2)$ composed of 8(24) terms. By using the basis expressions $\text{lag}1(\text{lag}2)$ is reduced to 6(18) terms.

Comments: 10 pages, Revtex; Some misprints corrected, results unchanged