  This paper describes a tentative relativistic quantum mechanics approach
inspired by Dirac's point-form, which is based on the physics description on a
hyperboloid 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
delta 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.
