Scalars coupled to fermions in 1+1 dimensions

Using a method introduced in an earlier paper, we study a Bose field coupled to a Fermi field in 1+1 space-time dimensions. We employ the standard Hamiltonian formalism in which one computes the eigenvalues and eigenvectors of the Hamiltonian matrix. The matrix elements are computed using states defined on a lattice in momentum space. The results are compared with known strong and weak coupling limits. Bound states and renormalization effects are studied. We find that the choice of bare masses which give specified physical masses can be non-unique once a critical couplingλ _μ has been exceeded.