Relativistic Model Field Theory

A relativistic generalization of the Lee model is constructed and solved in the first sector. The solubility is achieved with an indefinite metric and a redefinition of antiparticle operators which amounts to a selection rule prohibiting pair creation. The renormalization of the $V$-particle results in three dressed states, one of which is a ghost. The properties of these states and their dependence on cutoff and coupling strength are discussed. The effects of various modifications of the interaction are analyzed. Thirdly, the $N-\theta$ scattering problem is solved exactly.