A Two-Dimensional Relativistic Field Theory

A particular two-dimensional relativistic field theory is considered. In some limit as the masses of the theory go to zero it approaches the Thirring model. By means of a formal transformation of the field operators the Hamiltonian is reduced to that of a free field. An improved perturbation expansion can be written down, necessitating only wave function renormalization, and it appears that the renormalized theory is consistent. The $S$ matrix can be exhibited exactly, and though it leads to no physical scattering, it is not equivalent to the unit matrix. Finally the renormalized current operator is displayed as a suitable limit of products of the renormalized field operators. The form of the result clearly separates the consistency problem in quantum electrodynamics from that of the "photon mass."