Light front dynamics of few body systems

A brief review of light front dynamics is given, with emphasis on the interaction dependence of light front angular momentum operators. The ξ-picture approach for dealing with this interaction dependence is outlined. The ζ-picture employs an arbitrary lightlike four-vector ζ. The state vectors and the operators in the ζ-picture are related to those in the standard picture by a unitary transformation which depends on the unit vector u ̂ = -ζ/|ζ|, where ζ is the three-vector part of ζ. The Okubo-Glöckle-Müller approach for constructing direct interaction instant form models from quantum field theories is extended to light front dynamics in both the standard picture and the ζ-picture. This extension is applied to a toy model of the nucleon-nucleon and pion-nucleon systems, and it is shown that a natural approximation scheme arises which leads to Poincaré-invariant potential models for these systems. The validity of the approximations is justified by means of numerical calculations of S-matrix elements.