Perturbative Approach to NonrenormalizableTheories

Using a perturbatively nonrenormalizable and non-perturbatively finite example(delta-function-type potential in nonrelativistic quantum mechanics), we illustratethat one can develop a perturbative approach for a nonrenormalizable theory.The key idea is the introduction of an additional expansion parameter whichallows us to eliminate infinities from the perturbative expressions. The generatedperturbative series reproduce the expansion of the exact analytical solution.