The effect of different boost expressions is considered for the calculation of the ground-state form factor of a two-body system made of scalar particles interacting via the exchange of a scalar boson. The aim is to provide an uncertainty range on methods employed in implementing these effects as well as an insight on their relevance when an "exact" calculation is possible. Using a wave function corresponding to a mass operator that has the appropriate properties to construct the generators of the Poincaré algebra in the framework of relativistic quantum mechanics, form factors are calculated using the boost transformations pertinent to the instant, front and point forms of this approach. Moderately and strongly bound systems are considered with masses of the exchanged boson taken as zero, 0.15 times the constituent mass m, and infinity. In the first and last cases, a comparison with "exact" calculations is made (Wick-Cutkosky model and Feynman triangle diagram). Results with a Galilean boost are also given. Momentum transfers up to Q 2 = 100 m 2 are considered. Emphasis is put on the contribution of the single-particle current, as usually done. It is found that the present point-form calculations of form factors strongly deviate from all the other ones, requiring large contributions from two-body currents. Different implementations of the point-form approach, where the role of these two-body currents would be less important, are sketched.

The electromagnetic form factor of the pion is calculated in the "point-form" of relativistic quantum mechanics using simple, phenomenological wave functions. It is found that the squared charge radius of the pion is predicted one order of magnitude larger than the experimental value and the asymptotic behavior expected from QCD cannot be reproduced. The origin of these discrepancies is analyzed. The present results confirm previous ones obtained from a theoretical model and call for major improvements in the implementation of the "point-form" approach.PACS numbers: 13.40. Gp, 12.39.Ki, 14.40.Aq * Electronic address: desplanq@isn.in2p3.fr † Electronic address: Lukas.Theussl@uv.es 1 As it has been observed in our recent work [16,17,18] and in Ref. [19], this implementation is not identical to the form proposed by Dirac [20] in that it does not involve a quantization performed on a hyperboloid. To emphasize this difference, we will put the expression "point-form" between quotation marks throughout this paper.

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It is known that binding energies calculated from the Bethe-Salpeter equation in ladder approximation can be reasonably well accounted for by an energy-dependent interaction, at least for the lowest states. It is also known that none of these approaches gives results close to what is obtained by using the same interaction in the so-called instantaneous approximation, which is often employed in non-relativistic calculations. However, a recently proposed effective interaction was shown to account for the main features of both the Bethe-Salpeter equation and the energydependent approach. In the present work, a detailed comparison of these different methods for calculating binding energies of a two-particle system is made. Some improvement, previously incorporated for the zero-mass boson case in the derivation of the effective interaction, is also employed for massive bosons. The constituent particles are taken to be distinguishable and spinless. Different masses of the exchanged boson (including a zero mass) as well as states with different angular momenta are considered and the contribution of the crossed two-boson exchange diagram is discussed. With this respect, the role played by the charge of the exchanged boson is emphasized. It is shown that the main difference between the Bethe-Salpeter results and the instantaneous approximation ones are not due to relativity as often conjectured.

It is shown that field-theory based single boson exchange potentials cannot be identified to those of the Yukawa or Coulomb type that are currently inserted in the Schrödinger equation. The potential which is obtained rather corresponds to this current single boson exchange potential corrected for the probability that the system under consideration is in a two-body component, therefore missing contributions due to the interaction of these two bodies while bosons are exchanged. The role of these contributions, which involve at least two boson exchanges, is examined. The conditions that allow one to recover the usual single boson exchange potential are given. It is shown that the present results have some relation: i) to the failure of the Bethe-Salpeter equation in reproducing the Dirac or Klein-Gordon equations in the limit where one of the constituent has a large mass, ii) to the absence of corrections of relative order α log 1 α to a full calculation of the binding energy in the case of neutral massless bosons or iii) to large corrections of wave-functions calculated perturbatively in some light-front approaches.