Relativistic bound states: a mass formula for vector mesons

The problem of interaction in relativistic quantum mechanics remains certainly one of the most attractive in particle physics. Interesting approaches have been proposed by DmAC (~), BAKA~IJIAN and THOMAS (2) and FOLDY (3). More recently some hope was born with the development of theories at infinite momentum (4), using the nonrelativistic structure of the Poincar4 group; but, if the success of such an approach is evident in the current algebra scheme, its use for describing interacting relativistic systems in the general case seems still uncertain. The success of the theory of quarks in hadron physics is one of the motivations for the interest of a relativistic description of bound states. The concept of quarks prisoner of hadrons they build up has led physicists to introduce appealing notions such as colour, gluon theory and more recently bag theories. To these attempts one must add the symmetric harmonic-oscillator quark model (5) for baryons in which quarks constituting baryons are assumed linked by harmonic-oscillator forces (**): first presented in the nonrelativistic scheme (7), its generalization to the relativistic case (s) does not appear so easy. Note at this point a recent paper (9) in which a model for relativistic bound-state perturbation theory is presented. However, it appears very important to have a relativistic t reatment of quarks. Let us recall the transformation from current to constituent quarks obtained by MELOSH (10) in a relativistic free quark model: this transformation can be simply interpreted as a Wigner's rotation (~), and so could not appear in a nonrelativistic t reatment .