APH N.S., Heavy Ion Physics 16/1–4 (2002) 27–34 HEAVY ION PHYSICS c Akad´ emiai Kiad´ o Renormalization in Few-Body Nuclear Physics L. Tomio, 1,a R. Biswas, 1 A. Delfino 2 and T. Frederico 3 1 Instituto de F´ ısica Te´ orica, UNESP, 01405-900, S˜ ao Paulo, Brasil 2 Instituto de F´ ısica, Universidade Federal Fluminense, Niter´ oi, Brasil 3 Instituto Tecnol´ ogico de Aeron´ autica, CTA, 12228-900, S.J. dos Campos, Brasil Received 15 October 2001 Abstract. Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). They express the renormalization group in- variance of quantum mechanics. The present approach for the renormalization scheme relies on a subtracted T-matrix equation. Keywords: renormalization, renormalization group, Hamiltonian approach, scattering theory PACS: 03.65.Ca, 11.10.Hi, 11.10.Ef, 03.65.Nk 1. Introduction The interest in the application of effective theories to represent a more fundamental theory, as Quantum ChromoDynamics (QCD), has increased recently. The program suggested in Ref. [1] is of particular interest, as it allows one to parameterize the physics of the high momentum states and work with effective degrees of freedom. The idea is to use an effective renormalized Hamiltonian that, in the interaction between low-momentum states, includes the coupling with high momentum states. The renormalized Hamiltonian carries the physical information contained in the quantum system in states of high momentum. In the nuclear physics context, the use of effective interactions containing singularities at short distances is motivated by the development of a chirally symmetric nucleon–nucleon interaction, which contains contact interactions (Dirac-delta and its higher order derivatives) [2]. Singular contact interactions have also been considered in specific renormal- ization treatments of scaling limits and correlations between low-energy observ- ables of three-body systems (in atomic and nuclear physics) [3–6]. A general non- perturbative renormalization procedure, via subtracted kernel, was proposed in Ref. [4], and applied to the one-pion-exchange potential supplemented by contact inter- 1219-7580/02/ $ 5.00 c  2002 Akad´ emiai Kiad´ o, Budapest