Front- and point-form dynamics of constituent quarks

Nowadays quantum chromodynamics (QCD) is considered as the fundamental theory of strongly interacting particles. The elementary building blocks of QCD are spin-1/2 quarks and spin-1 gluons. In order to explain the masses and the structure of the hadrons observed in nature in terms of quarks and gluons the QCD bound-state problem has to be solved. Although tremendous progress in this direction has been made by means of lattice formulations of QCD we are still far away from a satisfactory solution of the problem. On the other hand, (effective) constituent-quark models have turned out to be surprisingly successful in explaining hadron masses and their electromagnetic properties. With the introduction of constituent quarks the very complex quantum-field theoretical QCD bound-state problem is reduced to a much simpler quantum-mechanical one. Nevertheless, one is still confronted with the complication that light constituent quarks should be treated within a relativistic formalism. In order to benefit from ideas and concepts one is already familiar with from the non-relativistic case it is near at hand to use a Hamiltonian approach. The general problem of formulating relativistic Hamiltonian dynamics for a fixed number of particles goes back to the pioneering work of Dirac in which he suggested three different forms of relativistic dynamics, i.e. the instant-form, the front-form, and the point-form. These formulations of relativistic quantum mechanics differ from each other by the choice of the quantization surface and the interaction-dependence of the Poincare generators. The aim of the proposed project is to compare the front- and point-form formulations of relativistic few-quark systems with the goal that advantage can be taken from one or the other formulation, depending on the particular aspect of hadronic physics one wants to consider. The construction of current operators, e.g., is easier in point form, whereas contact to parton phenomenology is more conveniently made in front form. In order to avoid the problem of an interaction-dependent spin operator in front form and of a too complicated interaction dependence of the four-momentum operator in point form we will resort to the Bakamjian-Thomas approach in which the potentials are added to the invariant-mass operator (cf. Ref. [1]). Starting from quantum field theory, we will investigate the question how to derive relativistic meson-exchange potentials that can be applied within the Bakamjian-Thomas framework and still contain as much relativity as possible. Furthermore we will study the equivalence of the front- and point-form approach and the question of cluster separability in three-quark systems. We intend to study these issues on the basis of the chiral constituent-quark model (cf. Ref.[2]). It should, however, be mentioned that the answers to these questions are of more general importance (e.g. also for few-nucleon systems). As applications of our approach we will first consider simple quark-antiquark systems, like vector mesons, and in the sequel also baryons consisting of three-quarks. [1] B.D. Keister and W.N. Polyzou, Adv. Phys. 20, 225 (191). [2] L.Ya. Glozman et. Al., Phys. Rev. D58, 094030 (1998).