A New Picture for Light Front Dynamics, II

Abstract

The standard picture of light front dynamics employs the null plane ct + z = 0; whereas the new picture employs a set of null planes ξ · x = 0, where ξ is a lightlike vector. The state vectors and operators in the new picture, also called the ξ-picture, are related to the state vectors and operators in the standard picture by a unitary transformation which depends on the unit vector u = − ξ/|ξ|, where ξ is the three-vector part of ξ. The new picture provides a formalism for dealing with the interaction dependence that occurs in the transverse components of light front angular momentum operators. The present work extends the previous work with the same title to particles with spin. This extension is developed within the context of a two-particle model for the pion-nucleon system. This model is derived from a quantum field theory which describes the interaction between nucleons, pions, and sigma mesons through the virtual processes N ↔ N + π, π ↔ π + σ and N ↔ N + σ. The two-particle model is derived by extending to light front dynamics the Okubo-Glöckle-Müller approach for constructing direct interaction instant form models from quantum field theories. The two-particle light front model for pion-nucleon scattering is transformed to the ξ-picture and a set of coupled integral equations are solved numerically to obtain the s-wave pion-nucleon phase shifts. These numerical results justify an approximation for the two-particle interaction which when used in conjunction with a noninteracting two-particle spin operator leads to a Poincaré invariant potential model for the pion-nucleon system.