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

TL;DR

This paper demonstrates that incorporating space-time translation constraints in relativistic quantum mechanics approaches aligns predictions across different formalisms, reducing discrepancies in calculating system form factors.

Contribution

It shows that applying space-time translation constraints with suitable currents makes diverse RQM approaches yield identical form factor predictions.

Findings

Predictions become identical across various RQM approaches when constraints are included.

Numerical results support the theoretical equivalence for scalar particle systems.

The approach converges to a dispersion-relation method as a limit.

Abstract

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 "point-form" 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.