v 1 2 1 M ay 2 00 4 Relativistic quantum mechanics : A Dirac ’ s point - form inspired approach

This paper describes a tentative relativistic quantum mechanics approach inspired by Dirac's point-form, which is based on the physics description on a hy-perboloid surface. It is mainly characterized by a non-standard relation of the constituent momenta of some system to its total momentum. Contrary to instant-and front-form approaches, where it takes the form of a 3-dimensional δ(· · ·) function , the relation is given here by a Lorentz-scalar constraint. Thus, in the c.m. frame, the sum of the constituent momenta, which differs from zero off-energy shell, has no fixed direction, in accordance with the absence of preferred direction on a hyperboloid surface. To some extent, this gives rise to an extra degree of freedom entering the description of the system of interest. The development of a consistent formalism within this picture is described. Comparison with other approaches is made.