SPECIAL EXAMPLE OF RELATIVISTIC HAMILTONIAN FIELD-THEORY

We study fermion-boson bound and scattering states in a (3 + 1)-dimensional Yukawa theory, using a Tamm-Dancoff truncation of light-front field theory. We retain only two sectors of Fock space, the sector with one fermion and the sector with one fermion and one boson. Such truncations violate Lorentz covariance if one employs the canonical Hamiltonian. In order to restore covariance we modify the Hamiltonian, introducing new terms and allowing all terms to depend on the Fock-space sectors within which or between which they act. In this special example, which is closely related to the Lee model, simple sector-dependent mass and vertex counterterms are sufficient to yield finite observables that are exactly covariant for states whose invariant mass is less than a critical value determined by the cutoffs. Triviality prevents the complete removal of cutoffs from the Hamiltonian that we consider. This calculation illuminates several basic features of the renormalization program required by the nonperturbative light-front Tamm-Dancoff approach.