Poincaré-invariant Lee model

A relativistic generalization of the Lee model is developed within the framework of light-front dynamics. The model describes three particles V, N, and interacting through the virtual process VN+, with no antiparticles present. The model consists of ten generators which satisfy the commutation relations of the Poincaré group. The Lorentz invariance of the S-matrix elements that arise is demonstrated. The dressed V-particle state is given, and the integral equations that arise in the V-N sector are derived. The interacting spin operator for the model is analyzed in some detail. The integral equations for the V-N sector are transformed to a new picture and a partial-wave analysis of the transformed equations is carried out. It is shown that the V elastic scattering amplitudes can be obtained from the solution of uncoupled, one-dimensional integral equations. The model has many of the features of few-particle systems involving pions and nucleons and moreover provides insight into dealing with the interacting angular momentum operators of light-front dynamics.