Instant form dynamics of one particle exchange models.

Abstract

A general procedure for constructing instant form, one particle exchange models for two particle systems is developed. The procedure entails the construction of a mass operator which when used in conjunction with a free spin operator and a free Newton-Wigner position operator leads to an exactly Poincar\'e invariant model. The method is applied to a simple model for s-wave pion-nucleon scattering. This model is derived from a quantum field theory which describes the interaction between pions, nucleons, and sigma mesons through the virtual processes N?N+\ensuremath{\pi}, \ensuremath{\pi}?\ensuremath{\pi}+\ensuremath{\sigma}, and N?N+\ensuremath{\sigma}. The instant form version of this exchange model is compared with a front form version that was constructed previously. With the procedures used to ensure Poincar\'e invariance, the instant form two-particle potentials are of the same form as the front form potentials; however, the pion-nucleon propagators that appear in the two-particle Lippmann-Schwinger equations are not the same. The instant form and front form models are fit to the same s-wave pion-nucleon phase shifts, and the resulting parameters are compared.