I'm trying to understand how we might sum over the metric (or vielbein) in a QG theory. So I'm looking at a simple (perhaps too simple) 0+1D action. Imagine a scalar field in 0+1D. The vielbein in 0+1D would be have one component $e(t)$. Also we know that $\det(e(t))=e(t)$ and $g^{00}(t)=e(t)^2$....