I'm trying several very plain and extremely dumb ways to quantize gravity, including simply plugging several Dirac-style energy-momentum tensors into the field equation. I'm looking to find an untried way of tying the field equation up with field theory, including several harmonic approaches. For instance, coming up with a simple way of inverting the vacuum equation (that is, in treating the Riemannian side of the EFE as an operator).
Yes, this has been difficult, trivial in some places, and a partial waste of time; but it's certainly broadened my way of thinking about these things.
What I was most wondering is if anyone here has any insight into the Wheeler-Dewitt equation, which is actually what I've been studying for a few months. It's one area of my education which most professors entirely glossed over, which has long frustrated me.
I'm shooting in the dark in many ways, but as with some ventures, it's profited my understanding greatly, so if you just have an interesting calculation to suggest, that'd be fun.