Properties of few-body systems in relativistic quantum mechanics and constraints from transformations under Poincar\'{e} space-time translations

Abstract

Different approaches have been applied to the calculation of form factors of various hadronic systems within relativistic quantum mechanics. In a one-body current approximation, they can lead to results evidencing large discrepancies. Looking for an explanation of this spreading, it is shown that, for the largest part, these discrepancies can be related to a violation of Poincar\'e space-time translation invariance. Beyond energy-momentum conservation, which is generally assumed, fulfilling this symmetry implies specific relations that are generally ignored. Their relevance within the present context is discussed in detail both to explain the differences between predictions and to remove them.