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Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach

The transition form factor for electrodisintegration of a two-body bound system is calculated in the Bethe-Salpeter framework. For the initial (bound) and the final (scattering) states, we use our solutions of the Bethe-Salpeter equation in Minkowski space which were first obtained recently. The gauge invariance, which manifests itself in the conservation of the transition electromagnetic current Jq = 0, is studied numerically. It results from a cancellation between the plane wave and the final state interaction contributions. This cancellation takes place only if the initial bound state BS amplitude, the final scattering state and the operator of electromagnetic current are strictly consistent with each other, that is if they are found in the same dynamical framework. A reliable result for the transition form factor can be obtained in this case only.