On the Inequivalence of Renormalization and Self-Adjoint Extensions for   Quantum Singular Interactions
  A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian. 
Horacio E. Camblong, Luis N. Epele, Huner Fanchiotti, Carlos A. Garcia   Canal, Carlos R. Ordonez