It is not difficult to quantize weak gravity. This is usually written as a bimetric theory g_{ab} = η_{ab} h_{ab}, where η_{ab} is a flat spacetime (Minkowski) metric and h_{ab} is a perturbation on to of flat spacetime. We may write a theory of the sort g_{ab} = (e^{ω})_a^c η_{cb}, where the bimetric theory is to O(ω) in a series expansion
g_{ab} =~ (δ_a^c ω_a^c) η_{cb}.
Gravitons enter in if you write the perturbing metric term as h_{ab} = φ_aφ_b, or ω_a^c = φ_aφ^c. The Ricci curvature in this weak field approximation is
R_{ab} - (1/2)Tg_{ab} = □h^t_{ab},
with h^t_{ab} the traceless part of the metric, and □ the d'Alembertian operator. Which in a sourceless region this computes plane waves. The two polarization directions of the graviton may then be interpreted as a form of diphoton, or two photons in an entanglement or a "bunching" as in Hanbury Brown-Twiss quantum optical physics.
If we now think of extending this to a strong field limit there are the square of connection terms Γ^a_{bc} in the Ricci curvature, or cryptically written as R ~ ∂Γ ΓΓ where there is the appearance of the nonlinear quadratic term in the connection. This nonlinear term indicates the group structure is nonabelian, so the photon interpretation breaks down. The graviton in this case is a form of di-gluon, or gluons in a state entanglement or chain that has no net QCD color charge. This connects with the AdS_n ~ CFT_{n-1} correspondence, where for n = 4 the conformal field theory is quark-gluon QCD physics. Further D-branes have QCD correspondences and this takes one into the general theory I lay out. One does need to look at the references to learn more of the specifics. The quantum phase transition to entanglement states is given in the paper I write in ref 11 L. B. Crowell
The simple fact is that as physics develops it will invoke new mathematics. I don't think I am overly mathematical in this essay, and I leave most of those details in the references. A theoretical physicist I think is wise to have a decent toolbox of mathematical knowledge and thinking. Physics invokes ideas of symmetries, remember Noether: symmetry corresponds to conservation law, and invariant quantities can also have connections with topology and number theory. I think the more one is familiar with advanced mathematics the more capable one is of thinking deeply about these matters.
It is true that my work is commensurate with P. Gibbs'. If field theoretic locality and spacetime are emergent structures then so is causality. This emergence is connected with a quantum phase transition, or a quantum critical point (tricritical point of Landau), and something occurring on a scale much larger than the string length.
Cheers LC