Solving for the space-time metric in the QFT integrals

[Mike2]

I just heard that the cosmological constant is a coupling constant in some perturbative expansion of some QFT and can be interpreted as a mass? Is this true? Wouldn't that be interesting? That would mean that the GR effect of expansion may be responsible (or may be an equivalent expression for) QFT, right? Where can I learn more about this?

If this is correct, then there is now two ways to look at mass - as the coupling constant in QFT and as the mass matrix that is the metric that transforms between configuration space and phase space (Frankel's The Geometry of Physics, page 55). Since the coupling constant is solved for using the integrals of a perturbation expansion, is it possible to equate the coupling constant, which is a mass, to the metric, or its determinate, and equate this to the integral of the perturbation expansion, which also involves the metric in the integrand. Wouldn't this turn the metric into a dynamical entity to be solved for in the process? Or has this already been attempted? Or would this give us not enough equations to solve for the number of unknowns? Thanks.

[Mike2]

I just heard that the cosmological constant is a coupling constant in some perturbative expansion of some QFT and can be interpreted as a mass? Is this true? Wouldn't that be interesting? That would mean that the GR effect of expansion may be responsible (or may be an equivalent expression for) QFT, right? Where can I learn more about this?

If this is correct, then there is now two ways to look at mass - as the coupling constant in QFT and as the mass matrix that is the metric that transforms between configuration space and phase space (Frankel's The Geometry of Physics, page 55). Since the coupling constant is solved for using the integrals of a perturbation expansion, is it possible to equate the coupling constant, which is a mass, to the metric, or its determinate, and equate this to the integral of the perturbation expansion, which also involves the metric in the integrand. Wouldn't this turn the metric into a dynamical entity to be solved for in the process? Or has this already been attempted? Or would this give us not enough equations to solve for the number of unknowns? Thanks.
What I don't understand is whether this "mass matrix" which serve as a metric between configuration and phase space is applicable in general or even special relativity. And I'm not sure that the mass matrix can apply to one particle or does it only apply to many particles. Any help would be appreciated.

[Mike2]

What I don't understand is whether this "mass matrix" which serve as a metric between configuration and phase space is applicable in general or even special relativity. And I'm not sure that the mass matrix can apply to one particle or does it only apply to many particles. Any help would be appreciated.
If it can, I wonder if the coupling constant can be equated to the cosmological constant times the metric and then all this equated to a perturbation integral with the metric in it also, then does this constitute an eigenvalue problem with the cosmological constant as the eigenvalue? This is off the wall, so feel free to shoot it down. Thanks.