2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94960A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchangedHigh Energy Physics - TheoryHigh Energy Physics - PhenomenologyMathematical PhysicsNuclear TheoryQuantum Physicstext