Light-front Ward-Takahashi identity and current conservation

Abstract

We construct a conserved electromagnetic current for two-boson systems in finite mass boson exchange models within light-front dynamics. For that purpose, we use a quasipotential reduction to perform the three-dimensional light-front projection of the 4-dimensional current operator. The electromagnetic current operator acting on the valence component of bound and scattering states can be perturbatively calculated in the quasipotential expansion, in correspondence with a truncation of the Fock space. The divergence of the proposed current operator satisfies a Ward-Takahashi identity at any given order of the quasipotential expansion. Also shown is the relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter amplitudes and current for bound and scattering states with the 4-dimensional ones. The matrix elements of the 4-dimensional current operator can be fully recovered from the corresponding light-front ones. In one test case the theoretical framework is realized explicitly.