Current in the light-front Bethe-Salpeter formalism I: Replacement of non-wave function vertices

Abstract

We apply the light-front reduction of the Bethe-Salpeter equation to matrix elements of the electromagnetic current between bound states. Using a simple (1+1)-dimensional model to calculate form factors, we focus on two cases. In one case, the interaction is dominated by a term instantaneous in light-cone time. Here effects of higher Fock states are negligible and the form factor can be effectively expressed using non-wave function vertices and crossed interactions. If the interaction is not instantaneous, non-wave function vertices are replaced by contributions from higher Fock states. These higher Fock components arise from the covariant formalism via the energy poles of the Bethe-Salpeter vertex and the electromagnetic vertex. The replacement of non-wave function vertices in time-ordered perturbation theory is a theorem which directly extends to generalized parton distributions, e.g., in (3+1) dimensions.