One-loop corrections to tree diagrams

Motivated by quantum gravity (where multiloop and in particular one-loop corrections pose large problems) we study the zero-space dimension ψ⁴ model. A nonperturbative solution in the one-loop approximation for the relative vacuum amplitude is obtained. This amplitude is found to be nonanalytic in λ. This has possible implications for the gravity-modified quantum electrodynamics as proposed by Salam. The gravity Green's functions (at least the two-point functions) have a logλ-type behavior. We discuss why it is plausible that summation over all orders in perturbation theory may change this logλ dependence. We use an approximate connection between the Schwarzschild radius of the electron and the behavior in λ to suggest plausible effects of quantum-loop corrections on the Schwarzschild solution.