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

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.

arXiv comment26 pages, 3 figures, to be submitted

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Cited by in corpus (10)

• Quark-model study of few-baryon systems
• Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
• Electroweak properties of the $\pi$, $K$ and $K^{\ast }(892)$ in the three forms of relativistic kinematics
• Form factors in RQM approaches: constraints from space-time translations
• RQM description of the charge form factor of the pion and its asymptotic behavior
• Parity Nonconservation in Elastic $\vec{p}p$ Scattering
• Dirac's inspired point form and hadron form factors
• RQM description of PS meson form factors, constraints from space-time translations, and underlying dynamics
• Pion charge form factor and constraints from space-time translations
• Properties of few-body systems in relativistic quantum mechanics and constraints from transformations under Poincaré space-time translations