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Relativistic quantum mechanics: A Dirac's point-form inspired approach

B. Desplanques
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Abstract

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.

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B. Desplanques. 2004-05-21. Relativistic quantum mechanics: A Dirac's point-form inspired approach. https://doi.org/10.1016/j.nuclphysa.2004.10.015

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