https://hal.in2p3.fr/in2p3-00021902Desplanques, B.B.DesplanquesLPSC - Laboratoire de Physique Subatomique et de Cosmologie - UJF - UniversitĂ© Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - IN2P3 - Institut National de Physique NuclĂ©aire et de Physique des Particules du CNRS - Institut Polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche ScientifiqueRelativistic quantum mechanics : A Dirac's point-form inspired approachHAL CCSD2005[PHYS.NUCL] Physics [physics]/Nuclear Theory [nucl-th]bibliotheque, LPSC2004-06-07 15:30:572023-03-24 14:52:472004-06-07 15:30:57enJournal articles10.1016/j.nuclphysa.2004.10.0151This 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.