# Graviton propagator

1. Nov 23, 2007

### jdstokes

On page 36 of QFT in a nutshell, Zee sets an exercise to find the propagator for a massive spin 2 particle by assuming that it is a linear combination of terms such as $G_{\mu\nu}G_{\lambda\sigma}$. The only method I can think up for doing this is to write down all 36 products of $G_{\mu\nu},G_{\lambda\sigma},G_{\mu\sigma},G_{\mu\lambda},G_{\nu\sigma},G_{\lambda}$ and apply the symmetry operations to see which sum of terms is left invariant, likewise for the $G_{\mu\nu}k_\lambda k_\sigma$ terms.

Are there any slicker combinatorial methods for figuring this out or am I hoping for too much?