When considering diffusion of chemicals, the reaction part is business of chemical kinetics, where the relevant characteristics of different substances come from collision theory together with some classical statistics. If one want to go deep down, one can try to compute the collision rates with quantum theoretical methods.
For some time now I wonder if there is a reason that it might not be possible to just compute the whole chemical reaction process using a path integral. Can't one encode chemical substances (atoms to molecules) in a Hilber space'ish manner and come up with some sort of Lagrangian, mirroring the change of species concentration from one equilibirum (with seperated chemicals) to another?
$$"\ |CH_4,2 O_2 \rangle\ \ \overset{\text {burn}}\longrightarrow \ \ |CO_2, 2 H_2O\rangle\ "$$
Instead of iterating non-linear differential equations, which arise from classical statistical consideration, and which involve empircal or quantum chemically computed rate constants, can't one transfer all of this to computing Feynman diagrams? (Not implying that that would be easier.)
