Equivalence of Local and Separable Realizations of the   Discontinuity-Inducing Contact Interaction and Its Perturbative   Renormalizability
  We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization.   Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.Md 
Taksu Cheon (Kochi Tech), T. Shigehara (Saitama U) and K. Takayanagi   (Sophia U)