Why are we trying to quantize gravity but not to "gravitize the quantum"?

Question

It's probably needed to mention that I'm still a graduate student, so I studied both General Relativity and QFT but gravity was never mentioned in my QFT courses, nor the other way around. Nevertheless, from some independent study, it seems to me that the next step towards a TOE is always said to be a quantized theory of gravity, the search for a graviton, etc. 

My question is, couldn't the other way be useful to analyze as well? Has anyone tried to give a curved manifold representation of QFT? If so, has it failed? If not, how come we don't hear about it more often?

Comments

You may perhaps find this

https://arxiv.org/abs/gr-qc/9706069

helpful.

Answer 1

There's a lot in the literature about QFT on curved space time, but there are also books. Robert Wald's "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics" is from 1994, and already represents a review of such work over decades. Google gets you straight to the inevitable Wikipedia page https://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime. Follow the references in the books cited there and follow citations forward. You likely don't hear about this work much because it's usually done as an outgrowth of Local Quantum Physics/Algebraic QFT, which is outside the mainstream of ordinary interacting QFT (because it aims at mathematical rigor, which has failed insofar as there are still no interacting models in 3+1 dimensions.)