Coordinates in relativistic Hamiltonian mechanics

2005

Nuclear Physics A

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 instantand 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.

Section: • Change Of Variables In Different Formsmentioning

confidence: 99%

Section: • Change Of Variables In Different Formsmentioning

confidence: 99%

See 1 more Smart Citation

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

2005

Nuclear Physics A

“…We assume that the initial and final states are described on a unique hyperplane (in the "point form" of Bakamjian [18] and Sokolov [19], which involves hyperplanes perpendicular to the velocity of the system, two orientations should be introduced, which is manageable). From eq.…”

Section: Constraints From Covariance Under Space-time Translationsmentioning

confidence: 99%

Form factors in RQM approaches: Constraints from space-time translations

Dong

2008

Eur. Phys. J. A

Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current approximation, can lead to predictions with a very large range. It was shown that accounting for constraints related to space-time translations could considerably reduce this range. It is shown here that predictions can be made identical for a large range of cases. These ones include the following approaches: instant form, front form, and "pointform" in arbitrary momentum configurations and a dispersion-relation approach which can be considered as the approach which the other ones should converge to. This important result supposes both an implementation of the above constraints and an appropriate single-particle-like current. The change of variables that allows one to establish the equivalence of the approaches is given. Some points are illustrated with numerical results for the ground state of a system consisting of scalar particles.

“…Different versions may be nevertheless considered. The first one [3,4], extensively used in many works, is an instant form displaying the same symmetry as the point form ("P.F."). The second one [5] is more in the spirit of the Dirac point form, where physics is formulated on an hyperboloid surface (D.P.F.…”

Section: Form Factors In Different Forms: Single-particle Approximationmentioning

confidence: 99%

Form Factors in Relativistic Quantum Mechanics Approaches and Space-Time Translation Invariance

Few-Body Problems in Physics

2007

Invariance of form factors under Lorentz boosts is a criterion often advocated to determine whether their estimate in a RQM framework is reliable. It is shown that verifying relations stemming from covariance properties under space-time translations could be a more important criterion. Form factors calculated in different approaches for a simple system are discussed with these various respects. An approximate method is shown to remove the main discrepancies related to a violation of the above relations.