energy of 1 GeV above the nucleon mass the configurations of Table VI.2 : N, N+T, N+2n N+p, N+p+π We have included the A, which couples strongly to the one pion system (8AN~ 48NN) and the p meson which couples extremely strongly (g, ΔΝ to the pion system (g) ~ 58NTOUT. ρππ For the deuteron case we consider separately the configurations where the two nucleon orbitals yield an even or odd space symmetry respectively. For the even case all the listed 2N configurations can contribute without any pion except (Os0g). For the odd case at least one pion must be present. We also give between parenthesis the number of quanta for the NN and the nл configurations. The configurations are limited to six hw and by the parity and angular momentum requirements. The even space symmetry configurations are given in Table VI.3 and the odd space ones in Table VI.4. If the w and p are added we get in addition the Table VI.5. For the pion system we get likewise the configurations of Table VI.6 for a cut-off energy of about 1 GeV with our chosen oscillator parameter. n Thus we see on these various examples that the truncated spaces up to six pion masses (~1 GeV) are of moderate size. The complications introduced by the symmetrization problem are limited essentially to the s case, see section II.5.2 The only redundant configurational set which appears in the above ta3 bles is the very simple p case. Of course the effect of the cut-off energy on the low energy properties of the systems (form factors, electromagnetic moments etc...) has to be studied numerically. APPENDIX RELATIVISTIC KINEMATICS OF THE CENTER OF MASS We demonstrate in this appendix the result of Eq. (1.45), namely the C.M. coordinate R for a system of relativistic particles of energies E all con[8] sidered at an equal time is given by i then The discussion shall be carried out by considering successively the case of a single particle of mass M which decays into two others of masses and the case of two distinct particles of coordinates (x,t) and (x2t2). m2, my In the first case the C.M. trajectory is given by the trajectory of the initial particle M and we simply must compute the geometrical relations between that trajectory and the trajectories of the daughter particles. In a given reference system (S), see figure A.1, considering only the projections on the (xt) plane and assuming that the trajectory of the initial particle goes through the origin, the CM trajectory is |