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 $\theta$ interacting through the virtual process $V\rightleftarrows N+\theta$, 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 $\theta V-\theta \theta N$ sector are derived. The interacting spin operator for the model is analyzed in some detail. The integral equations for the $\theta V-\theta \theta N$ sector are transformed to a new picture and a partial-wave analysis of the transformed equations is carried out. It is shown that the $\theta V$ 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.