Perturbative renormalization in quantum few-body problems

As in quantum field theory, for some singular two-body potentials, the momentum-space perturbative treatment of the three-dimensional quantum N-body problem is shown to exhibit ultraviolet divergences. Renormalization of these models leads to a scale and finite observables. For a Dirac delta potential we carry on this renormalization for two- and three-body systems. A new divergence, and hence a new scale, emerges for each added particle. For N3 there are no divergences in one and two dimensions. The physical implications of these results are discussed. © 1995 The American Physical Society.