Current conservation in light front dynamics. - Josenilson Ádnei Oliveira Marinho (2007)
We adopt the quasi-potential method as a systematic tool to study relativistic composite systems projected at light-front global time hyperplanes. We address specifically the light-front projection of the Bethe-Salpeter equation for two-bosons, two-fermions and three-bosons systems. The quasi-potential formalism: i) provides a suitable framework for performing light front time projections, dealing with subtle specificities such as the instantaneous terms in fermion systems, and ii) allows one to subtract out the n-body light-front reducible diagrams. The light-front Ward-Takahashi identities for the electromagnetic current operator acting on the valence component of two-fermion and two-boson wave functions are discussed. We study current conservation considering as well the truncation of the quasi-potential expansion in powers of the 4-dimensional two-body irreducible interaction. A conserved electromagnetic current operator truncated in the quasi-potential expansion at a given order and consistent with the effective interaction is derived. A reverse light-front time operator that formally reconstructs the 4-dimensional Bethe-Salpeter amplitude from the valence wave function is derived. This operator can be calculated perturbatively in the quasi-potential expansion. We also show some practical applications of the formalism, exhibiting explicit examples and suggesting feasible and useful future applications.